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Number Theory Level pending

Let a , b , c , d a, b, c, d be 4 distinct positive integers such that a 2 + b 2 = c 2 + d 2 a^2+b^2=c^2+d^2 . Find the minimum value of a + b + c + d a+b+c+d .


The answer is 20.

Shubhang Mundra by Shubhang Mundra , 20, India

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1 solution

Shubhang Mundra
Jan 18, 2016

The smallest positive integer that is the sum of 2 squares of positive integers in ways being the smallest positive integer that is the sum of 2 squares of positive integers is 65.

1 2 1^{2} + 8 2 8^{2} = 65

4 2 4^{2} + 7 2 7^{2} = 65

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