A square number is an integer that is the square (i.e., second power) of another integer.

A square number, also called a perfect square, is a figurate number of the form S_n = n^2, where n is an integer. The square numbers for n = 0, 1, ... are 0, 1, 4, 9, 16, 25, 36, 49, ... (OEIS A000290). A plot of the first few square numbers represented as a sequence of binary bits is shown above. The top portion shows S_1 to S_255, and the bottom shows the next 510 values. The generating function giving the square numbers is (x(x + 1))/(1 - x)^3 = x + 4x^2 + 9x^3 + 16x^4 + ....

antisquare number | biquadratic number | Brocard's problem | Brown numbers | cannonball problem | Catalan's conjecture | centered square number | Clark's triangle | cubic number | Diophantine equation | Fermat's 4n+1 theorem | greedy algorithm | gross | heptagonal square number | Lagrange's four-square theorem | Landau-Ramanujan constant | octagonal square number | partition | pentagonal square number | pseudosquare | pyramidal number | squarefree | square triangular number | sum of squares function | Waring's problem

middle school level (California grade 7 standard)