How to Solve a Diophantine Equation | Integer Solutions?

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Комментарии
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Awesome...learned new thing today... I enjoyed it...👍🏻

nirajkumarverma
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Simon's Favorite Factoring Trick. 53 is prime with factors 1, 53 and -1, -53. Resulting in (0, 52), (52, 0) and (-2, -54), (-54, -2).

jim
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Hi Sybermath. I really enjoy your videos. I want to know if there is a similar method to solve if, 11a+ ab + 11b = 6436 or 11(a+b) + ab = 6436?. a and b are postive integers. Or generally,
c(a+b) + ab = x, where c and x are known. Other than adding a perfect square to both sides and factorizing, and then doing trial and error method.
Would be grateful if you can answer this.

sachinthaliyanage
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Special trick called s FFT, I was scared at this moment

Noobish_Monk
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a+b=S, ...risulta S^2+4S-208 un quadrato perfetto, ..S=52...S=-56

giuseppemalaguti
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Two methods basically the same. Factoring 53.

mcwulf
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On Friday I asked my math students “What are the factors of 52?” Silence…

OMG!

So I asked them how many suits there are in a deck of cards? They quickly answered: “spades, hearts, clubs, diamonds.” So I said, “Right, so that’s 4 suits. Now what’s 52 divided by 4.”
SILENCE…

what could these kids have been doing from Kindergarten to the end of 6th (or 7th) grade to be this terrible at arithmetic!?!?

THANK YOU!!!
(At least SOMEONE is still doing mathematics.)

STEAMerBear
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If a and b are to be integers (strictly), then only a + b = -54 is the only legal answer.
We know zero is not an integer.

Roq-stone