Prove that: (1213–1212+1211)(119–118+117) is divisible by 3, 7, 19, and 37.

It is only divisible by 3 but not divisible by 7, 19, and 37.

Step-by-step explanation:

The given expression is (1213 - 1212 + 1211)(119 - 118 + 117) and we have to prove whether this expression is divisible by 3, 7, 19 and 37 or not.

Now, the expression is (1213 - 1212 + 1211)(119 - 118 + 117)

= 1212 × 118

= 3 × 2 × 2 × 101 × 2 × 59 {Those are the prime factors of the expression}

Now, it is clear that the expression 1212 × 118 is only divisible by 3 but not divisible by 7, 19, and 37. (Answer)