How many pairs of squares, A and B, between 1 and 1,000,000 will satisfy the following equation? This is an assignment for our computer coding class. I realize that not many on this forum tackle question in computer programming. But any help from anybody would be greatly appreciated. Thank you very much.

A^2 + B^2 =1,863,702,780,625

Guest Feb 17, 2019

#1**+1 **

**I don't know what programming language you are learning. But, for this question, you would set up a simple search routine that would subtract A^2 or B^2 from the given number on the RHS and take its square root. If it returns an integer, then that is one number found. And so on****....**

**In C++ the routine would look something like this:**

**n=1; a=(2#(1863702780625 - n^2);b=if(ceil(a) - floor(a)==0, goto3, goto5);c=(2#(1863702780625 - n^2);print"n=",n, "=",c; n++;if(n<=1000000, goto1, discard=0;**

**With the above routine, my computer listed these numbers:**

**1 - 33292^2 + 1364769^2 2 -126945^2 + 1359260^2 3 -160055^2 + 1355760^2 4 -193060^2 + 1351455^2 5 -225960^2 + 1346345^2 6 -295008^2 + 1332919^2 7 -350175^2 + 1319500^2 8 -359639^2 + 1316952^2 9 -382249^2 + 1310568^2 10 -502460^2 + 1269345^2 11 -511560^2 + 1265705^2 12 -563745^2 + 1243340^2 13 -627039^2 + 1212652^2 14 -656425^2 + 1197000^2 15 -685412^2 + 1180641^2 16 -705628^2 + 1168671^2 17 -714000^2 + 1163575^2 18 -819105^2 + 1092140^2 19 -845495^2 + 1071840^2 20 -917112^2 + 1011241^2 21 -941500^2 + 988575^2 22 -965321^2 + 965328^2**

**Note: You have to be wary of duplicates!**

Guest Feb 17, 2019