Question

Method 1:
Remember: The product of ( n ) number of
consecutive positive integers is always divisible by ( n ! )
( therefore n^{3}-n=nleft(n^{2}-1right)=n(n+1)(n-1) )
( =(n-1) n(n+1) )
The above number: ( (n-1) n(n+1) ) is the product of three consecutive positive integers ( (n geq 2) ) which is divisible by ( 3 !=6 )
Hence, the number: ( n^{3}-n ) is divisible by 6 for
all positive integers ( n )

# 26. 11 Uie Sun Olle ZCIUCU, puuuuu f(x)= ax2+bx+c are equal, and the sum of coefficients is 2, then find a. 27. Find the largest single-digit number by which the expression n - n is divisible for all possible integral values of 28. If f(x) = ax + bx + c is divided by x, X-2 and x + 3, the remainders comes out to be 7. 9 and 49 find 122 +59 + 2)2

Solution