Diagonal Of A 4D Rectangular Prism
Find the number of quadruples of non-negative integers that satisfy the above equation.
The answer is 67.
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1 solution
Mathematica
Length@Reduce[a^2+b^2+c^2+d^2==100^2&&a>=b>=c>=d>=0,{a,b,c,d},Integers]returns 67
here are the quadruples
{{50, 50, 50, 50}, {56, 56, 52, 32}, {58, 58, 46, 34}, {62, 50, 50, 34}, {62, 54, 54, 18}, {62, 58, 46, 26}, {62, 62, 34, 34}, {62, 62, 46, 14}, {64, 48, 48, 36}, {64, 52, 40, 40}, {64, 56, 52, 8}, {64, 60, 48, 0}, {64, 64, 32, 28}, {66, 46, 42, 42}, {66, 62, 30, 30}, {66, 62, 42, 6}, {68, 64, 32, 16}, {70, 50, 38, 34}, {70, 50, 46, 22}, {70, 50, 50, 10}, {70, 62, 34, 10}, {70, 70, 10, 10}, {70, 70, 14, 2}, {72, 48, 44, 24}, {72, 64, 24, 12}, {74, 58, 26, 22}, {74, 58, 34, 2}, {74, 62, 22, 14}, {74, 62, 26, 2}, {76, 40, 40, 32}, {76, 56, 32, 8}, {76, 64, 8, 8}, {78, 46, 30, 30}, {78, 46, 42, 6}, {78, 54, 26, 18}, {78, 54, 30, 10}, {78, 62, 6, 6}, {80, 40, 40, 20}, {80, 44, 40, 8}, {80, 48, 36, 0}, {80, 56, 20, 8}, {80, 60, 0, 0}, {82, 38, 34, 26}, {82, 46, 26, 22}, {82, 46, 34, 2}, {82, 50, 26, 10}, {82, 54, 18, 6}, {84, 48, 24, 8}, {86, 38, 26, 22}, {86, 38, 34, 2}, {86, 46, 22, 2}, {86, 50, 10, 2}, {88, 40, 20, 16}, {88, 44, 16, 8}, {90, 30, 26, 18}, {90, 30, 30, 10}, {90, 42, 10, 6}, {92, 32, 16, 16}, {94, 22, 22, 14}, {94, 26, 22, 2}, {94, 34, 2, 2}, {96, 24, 12, 8}, {96, 28, 0, 0}, {98, 14, 10, 10}, {98, 14, 14, 2}, {98, 18, 6, 6}, {100, 0, 0, 0}}