Search a number
square numbers
square
Square numbers are numbers of the form  $n^2$  and can also be seen as simple figurate numbers (see picture aside).

Lagrange proved in 1770 that every number can be written as the sum of 4 square numbers.

Every number greater than 188 can be written as the sum of at most 5 distinct square numbers.

The sum of the reciprocals of square numbers is  $\pi^2/6$.

The first square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400 more terms

Square numbers can also be... (you may click on names or numbers and on + to get more values)

ABA 64 81 324 + 9986219369604 aban 16 25 36 + 1000000000000 abundant 36 100 144 + 49984900 alternating 16 25 36 + 987656329 amenable 16 25 36 + 999950884 apocalyptic 361 529 841 + 29929 arithmetic 49 169 361 + 9853321 automorphic 25 625 8212890625 binomial 36 1225 19600 + 1882672131025 brilliant 25 49 121 + 999002449 c.decagonal 361 116281 37442161 + 3882078149401 c.heptagonal 841 755161 678133681 + 546848356574521 c.nonagonal 1225 1413721 1631432881 1882672131025 c.octagonal 25 49 81 + 999999898700625 c.pentagonal 16 1156 22801 + 68366835443776 c.square 25 841 28561 + 43892069261881 c.triangular 64 361 6241 + 319312633001041 cake 64 576 67600 75203584 constructible 16 64 256 + 281474976710656 cube 64 729 4096 + 995686217814016 Cullen 25 Curzon 81 441 729 + 198218241 d-powerful 4225 4624 5329 + 9972964 de Polignac 40401 62001 96721 + 99620361 deceptive 237169 deficient 16 25 49 + 9991921 dig.balanced 49 169 225 + 199967881 droll 5184 57600 451584 + 994721136640000 Duffinian 16 25 36 + 9991921 eban 36 64 40000 + 64032004000000 economical 16 25 49 + 19998784 emirpimes 49 169 289 + 99460729 enlightened 256 2304 2500 + 274877906944 equidigital 16 25 49 + 19998784 eRAP 265225 616225 13213225 + 519926081481 esthetic 121 676 12321 + 123456787654321 evil 36 144 169 + 999824400 Fibonacci 144 Friedman 25 121 289 + 992016 frugal 256 625 729 + 999887641 gapful 100 121 225 + 99997618176 Gilda 49 happy 49 100 784 + 9966649 Harshad 36 81 100 + 10000000000 heptagonal 81 5929 2307361 + 350709705290025 hex 169 32761 6355441 + 46399815451081 hexagonal 1225 1413721 1631432881 1882672131025 highly composite 36 hoax 361 1600 2401 + 91011600 house 1175056 hungry 144 iban 100 121 144 + 774400 idoneal 16 25 impolite 16 64 256 + 281474976710656 inconsummate 441 1521 2601 + 962361 interprime 64 81 144 + 99880036 Jordan-Polya 16 36 64 + 989560464998400 junction 1024 2025 4624 + 99880036 katadrome 64 81 841 961 Leyland 100 lucky 25 49 169 + 9941409 Lynch-Bell 36 324 784 + 1382976 magnanimous 16 25 49 + 22801 metadrome 16 25 36 + 134689 modest 49 82369 312481 + 1666027489 nialpdrome 64 81 100 + 999887641000000 nonagonal 1089 8281 978121 + 708304623404049 nude 36 144 324 + 494439696 O'Halloran 36 oban 16 25 36 + 900 octagonal 225 43681 8473921 + 61866420601441 odious 16 25 49 + 999950884 palindromic 121 484 676 + 900075181570009 pancake 16 121 529 + 937385441796001 panconsummate 36 81 121 + 361 pandigital 225 38025 314721 + 9814072356 pentagonal 9801 94109401 903638458801 pernicious 25 36 49 + 9998244 persistent 1532487609 2081549376 3285697041 + 96438197025 plaindrome 16 25 36 + 277777788888889 Poulet 1194649 12327121 power 16 25 36 + 49999988518489 powerful 16 25 36 + 999999961946176 practical 16 36 64 + 9998244 prim.abundant 196 15376 342225 1032256 Proth 25 49 81 + 274878955521 pseudoperfect 36 100 144 + 1000000 repunit 121 400 Rhonda 15625 342225 115154361 5547121441 Ruth-Aaron 16 25 49 + 996383276100 Saint-Exupery 202500 12960000 147622500 + 961896108802500 self 64 121 400 + 999887641 semiprime 25 49 121 + 99460729 sliding 25 2500 250000 + 25000000000000 Smith 121 576 729 + 99281296 star 121 11881 1164241 + 107341182792481 strobogrammatic 6889 69169 109181601 super Niven 36 100 400 + 44100000000 super-d 81 169 784 + 9979281 superabundant 36 tau 36 225 441 + 998117649 taxicab 6080256576 49991146569 389136420864 + 781111665140625 tetrahedral 19600 triangular 36 1225 41616 + 63955431761796 tribonacci 81 3136 10609 trimorphic 25 49 625 + 8212890625 uban 16 25 36 + 98010099000025 Ulam 16 36 324 + 9796900 undulating 121 484 676 69696 unprimeable 324 625 1764 + 9972964 untouchable 324 576 784 + 984064 upside-down 64 45346756 68591524 + 43211599876 vampire 186624 19847025 21068100 + 5267275776 wasteful 36 100 144 + 9998244 Zuckerman 36 144 1296 + 6318342144 zygodrome 7744 774400 77440000 + 992255544007744