Question

若整数n可表示为n=(x+y+z)[(x-y)²+(x-z)²+(y-z)²]/2（x、y

Answer 1

思路：关键是在等式n=(x+y+z)[(x-y)²+(x-z)²+(y-z)²]/2的右边凑出来因式3k+1或3k+2或9k证明：取x=y=k,z=k+1,n=(k+k+k+1)[(k-k)²+(k-k-1)²+(k-k-1)²]/2=（3k+1）×（0+1+1）/2=3k+1即...