Two squares
Number Theory
Level
4
How many integers between 1 and 100 inclusive can be expressed as the sum of 2 perfect squares ?
The answer is 43.
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1 solution
The only thing I did was a brute force method. 0+1 through 0+100 -- 10 possibilities 1+1 through 1+ 81 -- 9 possibilities 4+4 through 4 + 81 -- 8 possibilities 9+9 through 9 + 81 -- 7 possibilities 16+16 through 16+64 -- 5 possibilities 25+25 through 25+64 -- 4 possibilities 36+36 through 36+64 -- 3 possibilities 49+49 -- 1 possibility Total: 47 possibilities However the following had a duplicate sum: 9+16 -- same as 0+25 25+25 -- same as 1+49 36+49 -- same as 4+81 36+64 -- same as 0+100
47 - 4 = 43 possibilities.