Three different ways
Computer Science
Level
5
Which is the second smallest integer that can be expressed as the sum of three squares in three different ways?
Image Credit: Wikimedia Centered Square Number by S.F Birkner
The answer is 54.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Mathematica
Select[Range@100,(s=#;Length@Select[PowersRepresentations[s,3,2],#[[1]]!=0&]==3)&][[1]]54
here are the three ways
{{1, 2, 7}, {2, 5, 5}, {3, 3, 6}}
other integers
{54,66,81,86,89,99,101,110,114,126,131,149,150,162,166,173,174,179,182,185,186,216,219,221,222,225,227,233,237,241,242,245,258,264,274,275,286,291,302,305,309,315,318,323,324,334,338,344,347,349,356,361,366,377,396,404,410,418,422,430,433,438,440,443,453,456,475,481,490,498,504,507,515,517,523,524,526,529,571,596,597,600,606,617,618,619,622,634,637,648,653,664,669,670,673,682,683,691,692,694,696,707,716,718,723,728,733,739,740,744,745,762,778,785,787,802,813,814,826,835,841,864,865,876,884,888,898,900,908,932,942,947,948,964,968,973,980,982,997}