证明：如果整数[tex=1.429x1.214]HCTRLtzxkeBZo1HKwKR3/g==[/tex]都能表示成形式为[tex=7.143x1.429]Wf83/73PGFjrj0KDF6guYbV6J8bLk4+QFiOJxK8vJCQ=[/tex]的数，那么[tex=1.0x1.0]HvPURMKHpMl7dabEGRl/2Q==[/tex]也能表示成这种形式的数.

2022-07-23

证明：如果整数[tex=1.429x1.214]HCTRLtzxkeBZo1HKwKR3/g==[/tex]都能表示成形式为[tex=7.143x1.429]Wf83/73PGFjrj0KDF6guYbV6J8bLk4+QFiOJxK8vJCQ=[/tex]的数，那么[tex=1.0x1.0]HvPURMKHpMl7dabEGRl/2Q==[/tex]也能表示成这种形式的数.

答案：

证明：[tex=20.643x3.5]Wf83/73PGFjrj0KDF6guYTwcZNGPFNtSzAKseGlY59J1cNSt00/Q69PJTSMLvgNrhbs3obGSrCUNzRsj5Tn17EGi/dEM75g4TnRm8E+hIFR2JnDi+W17PnlyLRxUmE19pNwZX+xFMQxFipVU0nbicj5+nkm6/KGJJe1Gpw0QCvOUrZVpK18dS1FOem52Y7nG[/tex]，其中[tex=7.786x3.5]XbmfowmH+x2njRlGmJod4qyIX0YGb65EDRHA4ojvMwEeJMXJK/HlIYoqHCi8Athpusr5L1pVKubrMS9koxt0vSsBonu8tYbLsud+XHTl5B+8I54WTBOFZO0/pMBLOhF2[/tex]是循环移位矩阵.且[tex=2.429x1.214]qe/zM4ReR9cpasdwBSiHYA==[/tex].设[tex=18.643x1.5]hgV8wooUM++vaN7YACQr27bTlgZR6RrsBuz+0HBQ5Y3OpfovUasNtC4WmAFiY4oira/bdY0A5XA68Un0lSoVQoZUoI/ZX+ErnQREG5oJNOLeUuhCVMr6THMeCJthnOGeqeoIO7LXptlEBArKYuLUbg==[/tex]，则[tex=16.143x1.571]AtlSD0Oo2hrhSAxGLdsi85AE3pvxYLz4WVB1vN4ajD47l/fXB89pgPGq9tJ5N/iLDfgLdynoRwOsyaG0jCKcG+E3j+FObF/75ydw/X16jc3RLxVCgvNlVCYe5J1bixTp[/tex][tex=16.357x1.571]t7Aq9yK9A3LDKsoGxILvt1O3JwcqEpLWQ7QWVMSoDiXk8p0faXFXJqLA9njDvMh/qPY2nbo0ma459ia41yZDbSnt+TSbpvYG+vazXBQLqGP4y+ZyZ9WrDKmlJxV1YoHm[/tex][tex=28.286x1.571]t7Aq9yK9A3LDKsoGxILvt/Loa+jtMMIEhXzie0LbbUuZyss2kdhO9F8HnPVY5hNa9aq4YjIlaXu1ZZsrwsz/xfJTCHISKMdDh8PhaKeBccjZNDKehHX9gWBgfE2XDw2JavzILWkmbTK8fXmmYl4NEP2cA6Ea043T1pYY0pgFm5WVjfDuaCbty2QafiYs50I1wIoQcVtp+wFu4bwjOfpTaOPYmpEtL4wuF3R8kZkkbI4=[/tex][tex=26.286x1.571]wuU0RTl9JX32CdBfroDpUWB/ZKZ0+gUMa+6sH1RrBFVB8oY58J9hX4kWPFDM4ODLk1qPmolYVB3o9SRN3JVCS3NBCJotl67UWBOL7MwSlE5s6xNQ/dFEiq+nHSn+ENwomsNPrQ03Z4OqY8RcPHnMj8hXXCN8oAhf9382OHd+AnFoYFaMWa4glAHFk0gAuaO/rMiQxXBs6gG4CeU/avKrTQ==[/tex][tex=23.714x1.357]hvCXyipDpkxNHG9S+iGfGw566Fr2ywZSfLQlFv+VIfelHpRjzSO/a7ccEiuNIIuHxp7PV2RRi1DQu02l22C3h6JT99hjn3MyhpeDCUUPocTo7tVGBkWh6PSKet+HSuS071kk57cnkEy/n82NrCLlUspkXHzBa0DvzGCH/kLcauw+sEayRFhpIY5UJfBBccf37dPCu6aM/cKkug4KaRDmRw==[/tex].

举一反三

内容

0
证明：如果[tex=1.0x1.0]0GU//5PJyC1ZogOpKG0U3A==[/tex]表示不是完全平方数的第[tex=0.643x0.786]SBMIs+VUk7//BOpfqlQl0w==[/tex]个正整数，则[tex=5.643x1.429]gf3D4+n4I+EACSWKQD1g4PJXlqFJHpyjMWHRGx2UAyo=[/tex]，其中[tex=1.571x1.357]ZsDgkYtYKqR3cxt0YkcOzQ==[/tex]表示最接近于实数[tex=0.571x0.786]c5VsltFnl9nO0qB/vNKOWA==[/tex]的整数。
1
应用凸函数概念证明如下不等式：（1）对任意实数[tex=1.429x1.214]HCTRLtzxkeBZo1HKwKR3/g==[/tex]，有[tex=7.214x2.357]Ce5H5HWeZoxpGv501xQvoayFviwvZfmUYPLq3kTYfhQKWvM16pJVjcGfbzSsXngGpWu4WzKODOkLp96bEnw+NRfkHrsuM5lHsOTDO7SB5IE=[/tex]
2
证明：函数[tex=6.357x1.357]8bUPxlHG5g4+SObqJD9MKA==[/tex]在全平面连续，其中[tex=1.429x1.214]HCTRLtzxkeBZo1HKwKR3/g==[/tex]为复常数.
3
设[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]是一元多项式，[tex=1.429x1.214]HCTRLtzxkeBZo1HKwKR3/g==[/tex]是任意数，[tex=0.5x0.786]EL0hSqs6jZBGdsmH7TMShQ==[/tex]是非零数，试证：1）[tex=9.071x1.357]YQBMD9AuWhXYc3lnwarsr2nfZ4nSbnsietXQyTV8dTsgUgpI0L+aorzpG8mwDZzA[/tex]是常数：2) [tex=13.357x1.357]a+BxhJtUaZmJTJc7xXT+jhaO1sQd9J7VvC2e3EZ9qD0CS0Pc/mXhUQVF99zvv1lG[/tex]([tex=0.571x1.0]CQkpoDeAAI+5FKIfe1wVCA==[/tex]为常数)；3）[tex=12.0x1.357]81MyJ6DNp2pbGPQ3+N/8husLiUusoRoxUyCJ0T60q1YCiIh1uk0QHzLjaBnE9ZzH[/tex]或[tex=0.5x1.0]oYgVDn+QZqcDCRxqEZwM2A==[/tex]
4
证明：如果[tex=2.643x1.357]wX5rxliQzaaiHxrmreSqsg==[/tex]和[tex=0.929x0.786]D9maNLyVVGrC3QbL9jjRWg==[/tex]为大于1的整数，并且如果[tex=6.5x1.357]sBfXW0o0XYzGYUVg21XLTkdW+CfQnC3ZhLcXy5i+TPs=[/tex]，其中[tex=1.429x1.214]UDzjWQOzN0EZEJXR2XShvQ==[/tex]为整数，则[tex=6.286x1.357]EfBqI4VqjKHoNuCZ6SDPKEmDBNoPiOGsKf3EiBtUzo4=[/tex]。