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证明多项式 f(x)=1/7x~7+1/5x~51/3x~3+34/105x当x取任何整数时,总是得整数。[证]当x=0时是对的,因为f(0)=0。假定当x=k(某一正整数)时,f(k)是整数,那末 f(k+1)=1/7(k+1)~7+1/5(k+1)~5+1/3(k+1)~3
Proof polynomial f(x)=1/7x~7+1/5x~51/3x~3+34/105x When x takes any integer, it is always an integer. [Certificate] It is true when x=0 because f(0)=0. Suppose f(k) is an integer when x=k(a certain positive integer), then f(k+1)=1/7(k+1)~7+1/5(k+1)~5+ 1/3(k+1)~3