Question

show that any positive odd integer is in the form of 4q + 1 where q is some integer, by using division algorithm​

Answer 1

Answer:

According to Euclid's division algorithm; a and b can be expressed as a = bq + r, where q is quotient and r is remainder and 0 ≤ r < b. r = 0 ⇒ a = 4q, which is divisible by 2 and so is even. r = 1 ⇒ a = 4q + 1, which is not divisible by 2 and so is odd. r = 3 Þ q = 4q + 3, which is not divisible by 2 and so is odd.