If the conjecture were true, it would be a generalization of Fermat's last theorem, which could be seen as the special case n = 2: if, then.

If the four-color conjecture were false, there would be at least one map with the smallest possible number of regions that requires five colors.

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

If, for some n, such an i doesn't exist, we say that n has infinite total stopping time and the conjecture is false.

If the strong Goldbach conjecture is true, the weak Goldbach conjecture will be true by implication.

This precept, from one of Bacchylides ' extant fragments, was considered by his modern editor, Richard Claverhouse Jebb, to be typical of the poet's temperament: " If the utterances scattered throughout the poems warrant a conjecture, Bacchylides was of placid temper ; amiably tolerant ; satisfied with a modest lot ; not free from some tinge of that pensive melancholy which was peculiarly Ionian ; but with good sense ..."

If Rivers ever did come to access the veiled memory then he does not appear to make a note of it so the nature of the experience is open to conjecture.

The conjecture is stated in terms of three positive integers, a, b and c ( whence comes the name ), which have no common factor and satisfy a + b = c. If d denotes the product of the distinct prime factors of abc, the conjecture essentially states that d cannot be much smaller than c.

If G, H are graphs, we define a map φ: E ( G ) —> E ( H ) to be cycle-continuous if the pre-image of every cycle of H is a cycle of G. A fascinating conjecture of Jaeger asserts that every bridgeless graph has a cycle-continuous mapping to the Petersen graph.

Haupt's critical work is distinguished by a combination of the most painstaking investigation with bold conjecture ; his oft-cited dictum that " If the sense requires it, I am prepared to write Constantinopolitanus where the MSS have the monosyllabic interjection o " well expresses this boldness.

If the Hodge conjecture holds for Hodge classes of degree p, p < n, then the Hodge conjecture holds for Hodge classes of degree 2n − p.

If this conjecture is correct, quipus are the only known example of a complex language recorded in a 3-D system.

If the conjecture is false, a counterexample would take the form of a graph with minimum degree three having no power-of-two cycles.

If π ( x ) is the number of primes up to and including x then the conjecture states that

If the first Hardy – Littlewood conjecture holds, then the first such k-tuple is expected for x greater than 1. 5 × 10 < sup > 174 </ sup > but less than 2. 2 × 10 < sup > 1198 </ sup >.

" Despite its simplicity, it suggests a deeper conjecture: " If is an algebraic extension and if every nonconstant polynomial with coefficients in F has a root in E, is E algebraically closed?

If a lower bound ( for the function value ) could be found for every one of these configurations that was greater than the value of the function for the cubic close packing arrangement, then the Kepler conjecture would be proved.

If the Birch and Swinnerton-Dyer conjecture was proved, Tunnell's theorem would give a full resolution to the congruent number problem.

If the conjecture is true, this would imply the nonexistence of odd perfect numbers.

If the unique games conjecture is true, then it is impossible to approximate MAX 2-SAT, balanced or not, with an approximation constant better than 0. 943 ... in polynomial time.

In mathematics, the Sato – Tate conjecture is a statistical statement about the family of elliptic curves E < sub > p </ sub > over the finite field with p elements, with p a prime number, obtained from an elliptic curve E over the rational number field, by the process of reduction modulo a prime for almost all p. If N < sub > p </ sub > denotes the number of points on E < sub > p </ sub > and defined over the field with p elements, the conjecture gives an answer to the distribution of the second-order term for N < sub > p </ sub >.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If it could be shown that judgments of good and bad were not judgments at all, that they asserted nothing true or false, but merely expressed emotions like `` Hurrah '' or `` Fiddlesticks '', then these wayward judgments would cease from troubling and weary heads could be at rest.

If either P or Q is true and P is false, then Q is true.

If liberty is taken to mean " the ability to exercise one's rights as provided for by the law and nature " then this is true, but if it means " the state when one is not held to nor required to perform anything against their will " then this is clearly false.

To show that the claim " If a is a philosopher then a is a scholar " is false, one would show there is some philosopher who is not a scholar.

* Italo Calvino's novel If On a Winter's Night a Traveller deals extensively with the concepts surrounding false documents, including serially representing the contents of the novel itself as a false document.

If Language A borrowed a word from Language B, or both borrowed the word from a third language or inherited it from a common ancestor, and later the word shifted in meaning or acquired additional meanings in at least one of these languages, a native speaker of one language will face a false friend when learning the other.

If a statement happens to be true in our world, but is false in some other worlds, then it is a contingent truth.

If false, it may reflect a desire to silence one of the greatest embarrassments to the Bush administration.

# If one commits a fallacy, one says something false or not worth serious consideration.

If " this sentence is false " is true, then the sentence is false, which would in turn mean that it is actually true, but this would mean that it is false, and so on ad infinitum.

If ( A ) is true, then " This statement is false " is true.

If ( A ) is false, then " This statement is false " is false.

If ( B ) is neither true nor false, then it must be not true.

If ( C ) is both true and false, then ( C ) is only false.

If " this statement is false " is denoted by A and its truth value is being sought, it is necessary to find a condition that restricts the choice of possible truth values of A.

If some statement, B, is assumed to be false, one writes, " B

If it is not raining outside, then is false ; and if there is no cold-front over Kansas, then is false.