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Wallis's Problem


Find nontrivial solutions to sigma(x^2)=sigma(y^2) other than (x,y)=(4,5), where sigma(n) is the divisor function. Nontrivial solutions means that solutions which are multiples of smaller solutions are not considered. For example, multiples m of (x,y)=(4,5) are solutions for m=3, 7, 9, 11, 13, 17, 19, 23, 21, ....

Nontrivial solutions to Wallis's equation include (x,y)=(4,5), (326, 407), (406, 489), (627, 749), (740, 878), (880, 1451), (888, 1102), (1026, 1208), (1110, 1943), (1284, 1528, 1605), (1510, 1809), (1628, 1630, 2035), (1956, 2030, 2445), (2013, 2557), (2072, 3097), (2508, 2996, 3135, 3745), ....


See also

Divisor Function, Fermat's Divisor Problem

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References

Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, pp. 54-56, 2005.

Referenced on Wolfram|Alpha

Wallis's Problem

Cite this as:

Weisstein, Eric W. "Wallis's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WallissProblem.html

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