If the ideals A and B of R are coprime, then AB = A ∩ B ; furthermore, if C is a third ideal such that A contains BC, then A contains C. The Chinese remainder theorem is an important statement about coprime ideals.

If the remainder is zero the answer produced is ' yes ', otherwise it is ' no '.

If f is a polynomial and p is big enough, then the remainder term vanishes.

# If the remainder from dividing N by 6 is not 2 or 3 then the list is simply all even numbers followed by all odd numbers ≤ N

# If the remainder is 2, swap 1 and 3 in odd list and move 5 to the end ( i. e. 3, 1, 7, 5 )

# If the remainder is 3, move 2 to the end of even list and 1, 3 to the end of odd list ( i. e. 4, 6, 8, 2-5, 7, 9, 1, 3 )

If b ≡ a ( mod n ), where n > 0, then if the remainder b is calculated

If is a natural number, then 1 and divide without remainder.

If such a condition does occur, the property reverts to the grantor, or a remainder interest is passed on to a third party.

If a senator died, resigned, or was expelled, the legislature of the state would appoint a replacement to serve out the remainder of the senator's term.

If that is not the case, then the remainder is called balloon maturity.

If you pick up the pile as a result of laying the last card in your hand, or laying one of your face up cards, then you may pick up the remainder of your face up cards.

If the Elder chooses to take fewer than the maximum, she may then look at the remainder from the five ( which are the first ones that the Younger will take ).

If the original sentence exceeded eight years, they were forced to stay as residents for the remainder of their lives and were provided land to settle on.

If a president is found guilty, he is removed from office and replaced by the vice president for the remainder of the term.

After Nag's Head landlord Mike was imprisoned for embezzlement in the episode " If They Could See Us Now ", Sid took over and kept that role for the remainder of the series.

If the head cloth remained in the same location as the remainder of the clothes, and if these remained where the body had been, it implies that Jesus ' body was lifted through the clothing, or that Jesus ' body de-materialised and re-materialised elsewhere, hence supporting more docetic interpretations.

: If there is no remainder the check digit is 0, otherwise the remainder value is subtracted from 11 to give the check digit:

* A large number of constituencies compared with the total number of seats — If too many seats are used for constituencies, the remainder are less likely to ensure strict proportionality.

If the fugitive eludes bail, the bondsman, not the bounty hunter, is responsible for the remainder of the fugitive's bail.

If a fictional treatment costs a total of GBP 45, 000 at today's value and increases a person's quality of life ( QoL ) from 0. 5 to 0. 6 for the remainder of their life from age 70 and onwards, and their expected lifespan increases from 73 to 75.

If the last remainder when we ran out of dividend digits had been something other than 0, there would have been two possible courses of action.

If R ( x ) is the remainder when P ( x ) is divided by ( x – r )< sup > 2 </ sup > — that is, by x < sup > 2 </ sup > – 2rx + r < sup > 2 </ sup > — then the equation of the tangent line to P ( x ) at x

If less than two years after his election, Somoza Garcia, defying the Conservative Party, declared his intention to stay in power beyond his presidential term.

* Video section of the website of the British Conservative Party, where " You Can Get It If You Really Want " was used as a campaign song

The ethnic minority communities were initially very unpopular with the white British population of Smethwick, prompting the election of Conservative Party Member of Parliament ( MP ) Peter Griffiths at the 1964 general election, in which the Labour Party MP was unseated following the campaign slogan " If you want a nigger for a neighbour, vote Labour " by his supporters.

Galley claimed that Green told him: “ If you are fired, we will look after you ”, but that his attempts to find work have been rebuffed ; Conservative MPs, Galley averred, “ don't want to touch me now that I have done their dirty work ”.

However the Conservative MP Rupert Allason was quoted in Searchlight magazine as saying " If they are against Maastricht, they can't be bad.

Labour leader Neil Kinnock employed the slogan: " If you want to vote Conservative, don't fall ill ".

If 80 % of Americans are getting better health care than we are in the UK then we ought to ask why, and we ought to ask how are we going to deliver equally good results .” The attacks by Helmer and Hannan led Conservative leader David Cameron to release a statement to the BBC saying: " The Conservative Party stands four square behind the NHS ,"

Robeson, however, was abruptly interrupted by a Conservative who asked Robeson " If the Republicans have done so much for the slaves, what have they done for their masters?

Moore criticized the December 2008 senate appointments of 18 Conservative loyalists by Prime Minister Stephen Harper saying ," With regard to the rumoured filling of the vacancies, you have to look at the motivation ... Is it just because he's afraid of losing government or is it because he wants the chamber to work, causing him to do his constitutional duty ?... If it does happen I'm pleased the Senate will be filled and the chamber can work properly as one of our two houses of Parliament ".

He was the only Conservative member of the Welsh National Assembly Advisory Group, and his work in relation to Welsh devolution was described by Dafydd Elis-Thomas ( Welsh Assembly Presiding Officer ) as " the most significant contribution of any Welsh Conservative politician to the cause of devolution ; If Ron Davies was the architect of devolution, Colwyn was his enthusiastic draughtsman.

* February 1974: Conservative Party, led by Edward Heath, " If they want the resolution that they will win through one day ... then there is no alternative to Mr Heath.

If the Soviet leadership had the power to appoint regional officials, they had the indirect power to elect the delegates of the Party Congresses.

If the right wing wants a fight, they are going to get it ... before I end up, either this Republican Party will reflect progressivism or I won't be with them anymore.

If passed, this would have given a government the power to introduce a bill proposing to ban the Communist Party.

If the Party chose, all its people could live in luxury, but they instead choose to lower the quality of living: It is important that the lower classes remain stupefied by poverty and the struggle for mere survival ; if they were to become too comfortable, they might learn to think for themselves and rebel against the Party.

If Zhao was unable to turn things around rapidly, a showdown with the Party conservatives would be all but inevitable.

At the 2005 Parliamentary Press Gallery Dinner ( typically a satirical event ), Layton sent up himself and his party, playing guitar and singing three songs ; " Party for Sale or Rent " ( to the tune of " King of the Road "), a re-worked version of " Nobody Knows You When You're Down and Out " with different humorous lyrics, and " If I Had Another $ 4. 6 Billion ".

If the party vote for the Māori Party had been more in proportion with the constituency seats won, there would have been a normal 120-member house.

If you know a Liberal Party that is not listed, you are encouraged to add it.

If it failed, it would be a failure only for the Party militants.

When asked in a 2001 Canadian Broadcasting Corporation documentary on the resurgence of the PC Party if he would ever consider running for the PC leadership, MacKay quipped, " If there's one thing I've learned in politics it's ' never say never.

He would be responsible for the greatest wound the Party has received since it was a Party ... If the Bill were now withdrawn, the whole present difficulty in our Party would be gone ".

If on the occasion of a conflict of the nature mentioned in Article 2, or at a time when neither of the Contracting Parties is engaged in warlike operations, a coalition is formed between third Powers with a view to the economic or financial boycott of either of the Contracting Parties, the other Contracting Party undertakes not to adhere to such coalition.

" If there are atheists and infidels in the Socialist Party, it is not the fault of Socialism.

The breakaway Scottish Labour Party considered recruiting him, but its leader Jim Sillars said: " If we have that chap in he'll be taking time away from me on the box ".

If you know a Socialist Party that is not listed, you are encouraged to add it.

Season two's " It's My Party And You'll Die If I Want You To " featured Freddy attacking a high school prom date who stood him up twenty years earlier.

The quantity and accessibility of the minigames was lauded by GameSpot, although the reviewer Ryan Davis proceeded to note " If you bought Mario Party 4 last year, Mario Party 5 is hard to recommend.