detailed solution

3. Prove that if n is a triangular number, then so are 9n + 1, 25n + 3, and 49n + 6. Hint: Recall that in the formula for finding the n-th triangular number, the numerator is a product of two consecutive integers. 4. A palindrome number is a number that remains the same when its digits are reversed. For example, the following numbers are palindromes: 7 22 131 5665 10 901 480 084. Show that a palindrome with an even number of digits is divisible by 11. Hint: Read your notes