2x²+2x+1/2=2(x²+x+1/4)=2(x+1/2)²
(x²-2xy+y²)+(-2x+2y)+1=(x-y)²-2(x-y)+1=(x-y-1)²
2(x-y)²+(y-x)=(x-y)(2x-2y-1)
25^7-5^12 =5^14-5^12=5^12(25-1)=24*5^12=24*5*5^11=120*5^11,可见,120为此式的因子,原式可被120整除.
2^48-1=(2^24+1)(2^24-1)=(2^24+1)(2^12+1)(2^12-1)=(2^24+1)(2^12+1)(2^6+1)(2^6-1)=(2^24+1)(2^12+1)*65*63, 可见这两个数是63和65