Observe 4

Number Theory Level 2

a a , b b , c c , d d , and e e are distinct positive integers greater than 1 1 such that a 2 + b 2 = c 2 + d 2 = e a^2+b^2=c^2+d^2=e .

What is the smallest possible value of e e ?


The answer is 85.

Mr. India by Mr. India , 17, India

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1 solution

Mr. India
Mar 2, 2019

85 = 9 2 + 2 2 = 7 2 + 6 2 85=9^2+2^2=7^2+6^2

I would love to see if someone has any interesting information about such numbers.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

If you want, try this problem and this problem . Your four problems inspired me to make them.

Joshua Lowrance - 2 years, 3 months ago

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Thank you!

Mr. India - 2 years, 3 months ago

@Mr. India For some interesting information, have a look at this paper .

Brian Charlesworth - 2 years, 3 months ago

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Thank you!

Mr. India - 2 years, 3 months ago

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