Remainders Basics — CAT Previous-Year Questions

Let A be the largest positive integer that divides all the numbers of the form 3^k + 4^k + 5^k and B be the largest positive integer that divides all the numbesr of the form 4^k + 3(4^k) + 4^k+2, where k is any positive integer. Then (A + B) equals

If A = {6²ⁿ - 35n - 1: n = 1, 2, 3, ...} and B = {35(n - 1) : n = 1,2,3,...} then which of the following is true?

If x = (16³ + 17³ + 18³ + 19³), then x divided by 70 leaves a remainder of

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

A certain number, when divided by 899, leaves a remainder 63. Find the remainder when the same number is divided by 29.