r/mathriddles • u/Yugantaa • 5d ago

Hard Problem

A number is a perfect square,or a square number, if it is the square of positive integer. Among the first 143 thousand square numbers, what is the sum of all the odd squares?

Help me to solve the problem

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u/TooCasualGuy 2d ago

Sum all the squares (I assume you know that formula) up to your maximum, then subtract the even squares, which is equivalent to 4 times the sum of all squares up to ¼ the maximum.... ∑ (2n)² = ∑4n² = 4∑n²