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完全平方数的十位数字与个位数字有着如下一种美妙的关系: 如果完全平方数的十位数字是奇数,则它的个位数字一定是6;反之,如果完全平方数的个位数字是6,则它的十位数字一定是奇数。下面我们先把这种关系证明一下,然后再看它的应用。先证前者,若已知m~2=(2k+1)。10+a,我们来证明a=6。因为完全平方数末尾数只可能是0,1,4,5,6,9,故这里的a只可能为0,1,4,5,6,9。当a=0时,m的末尾数为0,于是可设m=10n,那么(2k+1)。10=(10n)~2=100n~2,即2k+1=10n~2。
The ten-digit number of complete squares has a wonderful relationship with the one-digit number as follows: If the tens digit of the complete square is an odd number, its ones digit must be 6; otherwise, if the complete square is a single digit Yes 6, then its tens digit must be odd. Here we first prove this relationship, and then see its application. Proofer the former, if m~2=(2k+1) is known. 10+a, let’s prove a=6. Because the number of the end of the complete square can only be 0,1,4,5,6,9, a here may only be 0,1,4,5,6,9. When a = 0, the end of m is 0, then m = 10n, then (2k + 1). 10=(10n)~2=100n~2, that is, 2k+1=10n~2.