Sum of squares

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This applet finds the decomposition of any positive number greater than 1 into up to four squares.

Notice that it does not find the prime factorization of the number entered by the user, so some cases where two squares would be enough will be represented as a sum of three squares. For example, 10000998089 = 95317² + 30260².

If you find any error or you have a comment, please fill in the form.

You can also enter expressions that use the following operators and parentheses:

• + for addition
• - for subtraction
• * for multiplication
• / for integer division
• ^ for exponentiation
• n!: factorial
• p#: primorial (product of all primes less or equal than p).
• B(n): Previous pseudoprime to n
• F(n): Fibonacci number F_n
• L(n): Lucas number L_n = F_n-1 + F_n+1
• N(n): Next pseudoprime to n
• P(n): Unrestricted Partition Number (number of decompositions of n into integer summands without regard to order).

See the methods used in this applet here.