Using the above rule, we can complete the proof of Fermat's little theorem quite easily, as follows.

Using fortresses can be a good plan, but Machiavelli says he shall " blame anyone who, trusting in fortresses, thinks little of being hated by the people ".

Using two ropes runs little risk of getting tangled together, but using three significantly increases this risk.

Using the geometric product the formula is a little simpler

Using the traditional end product testing method, it was soon realized that almost all of the food manufactured was being used on testing and very little was left for actual use.

Using eigenfaces is very fast, and able to functionally operate on lots of faces in very little time.

Using underpasses as protection does little more than raise people above ground level, exposing them to higher winds and more debris.

Using don't cares can simplify decision tables, especially when a given condition has little influence on the actions to be performed.

Using portable equipment and requiring little or no set up time, the New Wave way of filmmaking presented a documentary type style.

Using a little of his Christmas magic, he livens it up by presenting everyone with their childhood dream gifts ( much like he did for Laura and Neil in the first film ).

Using this sociologically-based theory has little to no link to the benefit of psychology due to its weakness in operational definitions and weak analytical mode.

Using the bracelet and a little help from an inside ally, the group locates the source of the problem and proceed to stop it.

Using what little Energon he had left, Alpha Q recreated another victim of Unicron – Starscream.

* Zero Rotation: Using a specific type of grip & release it is possible to impart little or no rotation on the ball.

Using an extremely sharp knife or tantō, the person cuts off the portion of his left little finger above the top knuckle on the finger or the tip of the finger.

Using the powers of some animals is necessary, while others simply make things a little easier.

Using aircraft as little as possible, the whole trip lasted 5½ months.

Using fast-reacting wire-guided or radio-command missiles meant the total engagement time was kept to a minimum, as there was little or no " lock-on " time required ; the operator simply fired and adjusted the missile's flight path onto the target while it flew.

Using these chemical processes films can be ready for collection in as little as 20 minutes, depending on the machine capabilities and the operator.

Using what little resources he can scrounge up, he devises a plan to sneak back into Spengo's palace and save Marge.

Using the image projections, extensive sound design, shadowplay, brief scenes, and " little man " character ( here, a patient embodying all syphilis sufferers throughout history ) made standard by the New York Unit, Spirochete followed syphilis from its introduction in Europe in the 15th century through to the social stigma surrounding it in the 1930s.

Using the British campaign against the Atlantic slave trade as their case study, Pape and Kaufmann seek to understand why Britain would unilaterally pursue a course of action that for decades incurred costs both economic and strategic with little or no benefits gained.

Using a little spaceship, the player goes into the computer's " Inner Space " to collect the uninfected icons and stop the Inner Demon, while simultaneously improving his ship and maintaining relationships with the population of Inner Space.

* Using the Gameshark code which enables all cars to be available for purchase from the start of the game causes extra cars to become available that so far have not been found through any other method and there appears to be very little information online about these hidden cars.

Using a linear velocity of 1. 2 m / s and a track pitch of 1. 5 µm yields a playing time of 80 minutes, or a data capacity of 700 MB.

Using a variety of specifications of the employment and unemployment equations ( using ordinary least squares vs. generalized least squares regression procedures, and linear vs. logarithmic specifications ), they found that a 10 percent increase in the minimum wage caused a 1 percent decrease in teenage employment, and no change in the teenage unemployment rate.

Using the known ionic radii for the trivalent rare earths and the linear correlation of log distribution coefficient with ionic radius, an average ionic radius of 0. 089 nm was estimated for Md < sup > 3 +</ sup > and a heat of hydration of –( 3654 ± 12 ) kJ / mol calculated using empirical models and the Born-Haber cycle.

Using an augmented matrix and an augmented vector, it is possible to represent both the translation and the linear map using a single matrix multiplication.

Using big-O notation, the performance of the interpolation algorithm on a data set of size N is O ( N ); however under the assumption of a uniform distribution of the data on the linear scale used for interpolation, the performance can be shown to be O ( log log N ).

Using a simple linear search on first occurrence and using a cached result thereafter is an obvious compromise.

Using the natural isomorphism between and the space of linear transformations from V to V ,< ref name =" natural iso "> Let L ( V, V ) be the space of linear transformations from V to V. Then the natural map

Using Maxwell's equations simultaneously with the curl of Ohm's Law, one can derive what is basically the linear eigenvalue equation for magnetic fields ( B ) which can be done when assuming that the magnetic field is independent from the velocity field.

Using multiple linear regression analyses, after adjusting for potential confounders, they claim betel consumption was statistically significantly associated with obesity.

Using iterative belief propagation techniques, LDPC codes can be decoded in time linear to their block length.

Using the Riesz representation theorem, one can show that there exists a unique continuous linear operator

Using a linear algorithm for unit propagation, the algorithm is linear in the size of the formula.

Using linear interpolation instead of quadratic interpolation gives the secant method.

* Using the source-filter model of speech production through linear prediction ( LP )( see the textbook " speech coding algorithm ");

Using matrix generators for linear programs revealed the importance of naming rows and columns in a consistent manner.

Using this as a basis, three different isotherms can be used to describe the binding dynamics of a column chromatography: linear, Langmuir, and Freundlich.

Using the simplex method to solve a linear program produces a set of equations of the form

Using PLAPACK — parallel linear algebra package.

Using linear probing, dictionary operation can be implemented in constant time.

Using a pivot language avoids the combinatorial explosion of having translators across every combination of the supported languages, as the number of combinations of language is linear (), rather than quadratic – one need only know the language A and the pivot language P ( and someone else the language B and the pivot P ), rather than needing a different translator for every possible combination of A and B.

Using linear regression, a line of best fit can now be calculated that describes how the reflection amplitude varies with offset using just 2 parameters: the intersect, P, and the gradient, G.