Olympiad Question | Solve Diophantine Equation 3^2x -2^2y-713=0 | Learn how to solve Olympiad easily

Can you solve the Diophantine Equation 3^2x -2^2y-713=0?

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Olympiad Question | Solve Diophantine Equation 3^2x -2^2y-713=0 | Learn how to solve Olympiad easily

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[nirupamasingh]

Vnice presentation in an easy way. Great help for students.

[rorydaulton]

You did not consider the possibility of factoring 713 into 713*1. This also leads to solutions for x and y, though they are not integers and thus not solutions to your problem. But this should at least be considered before being rejected.

[xyz]

It can be written as 9^x - 4^y = 713, and 9^x >713, as 9^3 = 729, 9^x - 4^y = 729- 16, hence x = 3 and y = 2

[fabatcazityt]

Thanks for this stimulating equation Mr 🥰🥰😚 you are the best

[messironaldo]

Should the question declare x, y are integers? Otherwise the answer is not the only solution while there are many solutions~

[monroeclewis]

I was delighted to get this one by applying the methods I learned in your previous lessons.

[HappyFamilyOnline]

Awesome explanation👍
Thanks for sharing🌹

[SuperYoonHo]

10th and 70th to like Thanks so much sir
love and praises may god bless you richly

[haoge]

does it need to metion "Integer solution" as a given condition?

[owlsmath]

Nice video sir! Love the exponential problems.

[mohamedabdelkaderahmed]

​ @PreMath Hello Dear have solved almost the same way you did till the step a^2-b^2=713
Then, as it's a difference between two squares so the closest no. is 729-16= (27)^2- (4)^2
so a=27, b=4 which implies x=3, y =2, thanks for you so much

[susennath]

excellent.

it can be guess by trial method.
my teacher tought me in 1990.
as 713 is a number corresponding power no 729, so we should follow power of 6 to the number 3 and 2^4 is 16 and so this is a trivial solution

[pezosdrare]

Is there a trick to easily find 713's factors ? Those prime numbers are annoying to find. I can easily find if there's any factor from 2 to 13 but then it becomes long :D

[stpat]

Other solution:
x = log base 3 of 357
y = log base 2 of 356

[konstantinjoukovski]

You haven't said that x and y must be integers. And if they are just rational numbers, there can be an unlimited number of solutions.

[ioannismichalopoulos]

Next time, you have to mention in the video that x and y are integers.

[miguelgnievesl]

I did it without substitutions. I didn't find it necessary.