√(n^2+√x)+√(n^2-√x)=m，求 x
本帖最后由 王守恩 于 2023-6-3 18:53 编辑已知正整数 n,m,满足\(\sqrt{n^2+\sqrt{x}}+\sqrt{n^2-\sqrt{x}}=m\), 求正整数 x。
n=01, 有0个解,
n=02, 有0个解,
n=03, 有0个解,
n=04, 有1个解, 最小m=06,x=000252,最大m=06,x=00252,
n=05, 有1个解, 最小m=08,x=000576,最大m=08,x=00576,
n=06, 有1个解, 最小m=10,x=001100,最大m=10,x=01100,
n=07, 有2个解, 最小m=10,x=002400,最大m=12,x=01872,
n=08, 有2个解, 最小m=12,x=004032,最大m=14,x=02940,
n=09, 有2个解, 最小m=14,x=006272,最大m=16,x=04352,
n=10, 有2个解, 最小m=16,x=009216,最大m=18,x=06156,
n=11, 有3个解, 最小m=16,x=014592,最大m=20,x=08400,
n=12, 有3个解, 最小m=18,x=020412,最大m=22,x=11132,
n=13, 有3个解, 最小m=20,x=027600,最大m=24,x=14400,
n=14, 有4个解, 最小m=20,x=038400,最大m=26,x=18252,
n=15, 有4个解, 最小m=22,x=050336,最大m=28,x=22736,
n=16, 有4个解, 最小m=24,x=064512,最大m=30,x=27900,
n=17, 有4个解, 最小m=26,x=081120,最大m=32,x=33792,
n=18, 有5个解, 最小m=26,x=104780,最大m=34,x=40460,
n=19, 有5个解, 最小m=28,x=129360,最大m=36,x=47952,
n=20, 有5个解, 最小m=30,x=157500,最大m=38,x=56316,
n=21, 有6个解, 最小m=30,x=194400,最大m=40,x=65600,
......
这里有5个数字串:
数字串(1)Table], {n, 1, 60}]
{0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17}
数字串(2)Table], {n, 4, 60}]
{6, 8, 10, 10, 12, 14, 16, 16, 18, 20, 20, 22, 24, 26, 26, 28, 30, 30, 32, 34, 34, 36, 38, 40, 40, 42, 44, 44, 46, 48, 50, 50, 52, 54, 54, 56, 58, 58, 60, 62, 64, 64, 66, 68, 68, 70, 72, 74, 74, 76,
数字串(3)Table]^2 - 4 Ceiling]^4, {n, 4, 60}]
{252, 576, 1100, 2400, 4032, 6272, 9216, 14592, 20412, 27600, 38400, 50336, 64512, 81120, 104780, 129360, 157500, 194400, 233472, 277440, 331772, 390096, 454860, 526400, 614400,
数字串(4)Table
{6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104,
数字串(5)Table
{252, 576, 1100, 1872, 2940, 4352, 6156, 8400, 11132, 14400, 18252, 22736, 27900, 33792, 40460, 47952, 56316, 65600, 75852, 87120,99452, 112896,127500, 143312,160380, 178752,198476, 我日，难道这个方程的解不是
\
吗？？？？？
Solve] + Sqrt] == m, {x}]
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