where there are a; + 1 options for each exponent x; because 0 ≤ x ≤ a,, and so the number of positive integer divisors is (a₁ + 1)(a₂ + 1)... (am + 1).

For each positive integer n, define an = 1/2 (C₂ (2 + √3)² + (2 − √3)”). - It is known that an is a positive integer for each n. Find the remainder when a2023 is divided by 4. (A) 0 (B) 1 (C) 2 (D) 3

Let a and b be integers, and let d be a positive common multiple of a and b. Show that the following two statements are equivalent.  (1) d <= c for every positive common multiple c of a and b. (2) d divides c for every common multiple c of a and b.

X || 6 [145]++84)]-[83] X 6 -7 = -6