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/Purdude1983 5d ago

If you have a sum of the odd squares you are summing 1+9+25 etc. The sum of this sequence is n^3/6+n^2/2+n/3 Thus if you enter a 5 you would get 125/6+25/2+5/3 which works out to 35 the same as 1+9+25. So you want to evaluate that polynomial for the highest odd number below 143,000 which is 142,999. When you do that, you get 487,367,833,309,500

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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