Observe 2

Number Theory Level 2

What is the value of smallest positive integer which can be written as the sum of two positive perfect squares in exactly 2 different ways?

Note: The perfect squares need not be distinct.


The answer is 50.

Mr. India by Mr. India , 17, India

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1 solution

Mr. India
Mar 2, 2019

50 = 7 2 + 1 2 = 5 2 + 5 2 50=7^2+1^2=5^2+5^2

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How do you show it is the smallest?

Henry U - 2 years, 3 months ago

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Honesty, I just did it by hit and try (as it wasn't difficult ). Can you prove it? ;-)

Mr. India - 2 years, 3 months ago

You should probably specify that the perfect squares must be positive, for otherwise the answer would be 25 25 since 0 2 + 5 2 = 3 2 + 4 2 = 25 0^{2} + 5^{2} = 3^{2} + 4^{2} = 25 .

Brian Charlesworth - 2 years, 3 months ago

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Done. Sorry if you faced some problem.

Mr. India - 2 years, 3 months ago

specify that theyre positive nonzero too

chase marangu - 2 years, 2 months ago

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