Question

show that the cube of any +ve integer is of the form 4m, 4m+1 or 4m+3, for some integer m​

Answer 1

Answer:

Let a be the positive integer and b = 4. Then, by Euclid's algorithm, a = 4q + r for some integer q ≥ 0 and r = 0, 1, 2, 3 because 0 ≤ r < 4. ... = 4m + 3, where m is some integer. Hence, The cube of any positive integer is of the form 4m, 4m + 1 or 4m + 3 for some integer m.