平方组成数

无心人

显然0,1,4,9是0,1,2,3的平方 注意到 144组成数字是1,4,4，且是12的平方 441，10404，40401也是 请问，是否还有数字具有 1、是某个整数的平方 2、10进制表示由0,1,4,9组成

无心人

由12*10^n 102*10^n 21*10^n 201*10^n组成的数字的平方都是这个性质 还有其他形式么？

gxqcn

A058414 Squares composed of digits {0,1,4}, not ending with zero. 1, 4, 144, 441, 1444, 10404, 40401, 1004004, 1100401, 4004001, 100040004, 114041041, 400040001, 414041104, 10000400004, 10110101401, 40000400001, 41011110144, 141001001001, 414441100441, 1000004000004, 1041110041104

A019544 Squares whose digits are squares. 0, 1, 4, 9, 49, 100, 144, 400, 441, 900, 1444, 4900, 9409, 10000, 10404, 11449, 14400, 19044, 40000, 40401, 44100, 44944, 90000, 144400, 419904, 490000, 491401, 904401, 940900, 994009, 1000000

A061270 Squares such that each digit is a square and the sum of the digits is a square. 1, 4, 9, 100, 144, 400, 441, 900, 10000, 10404, 14400, 40000, 40401, 44100, 44944, 90000, 1000000, 1004004, 1040400, 1440000, 4000000, 4004001, 4040100, 4410000, 4494400, 9000000, 9941409, 11909401, 100000000, 100040004, 100400400

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无心人

呵呵 还有更高的么？

gxqcn

这类数应该很容易被搜索到。

无心人

求出10^32内所有末位不是0的这类数字来

medie2005

21^2 == 441 94925771^2 == 9010901999944441 446653271^2 == 199499144494999441 221454271^2 == 49041994144141441 632534119159521^2 == 400099411900911111419444949441 137843911871729^2 == 19000944040100991144149449441

medie2005

下面列出$10^32$内，满足$a^2=n$，a的数字组成中不含0、n仅由{0,1,4,9}数字组成的n： 21^2 == 441 12^2 == 144 38^2 == 1444 212^2 == 44944 4462^2 == 19909444 6357^2 == 40411449 31488^2 == 991494144 317712^2 == 100940914944 971643^2 == 944090119449 387288^2 == 149991994944 94925771^2 == 9010901999944441 446653271^2 == 199499144494999441 221454271^2 == 49041994144141441 211992712^2 == 44940909941114944 6356918988^2 == 40410419019994944144 33452129143^2 == 1119044944199949914449 11832751643^2 == 140014011444919199449 64738643362712^2 == 4191091944444414491191994944 31481612751643^2 == 991091941444411141999199449 33318312524788^2 == 1110109949499444911114444944 632534119159521^2 == 400099411900911111419444949441 137843911871729^2 == 19000944040100991144149449441 3315269143525771^2 == 10991009494014099194444941144441 3176649241589462^2 == 10091100404090904111144149449444 2224645859254893^2 == 4949049199099941194941144441449 9536294568877893^2 == 90940914104409999119141144119449 一位的数就不列出了。 [ 本帖最后由 medie2005 于 2008-12-16 13:31 编辑 ]