Question

. Show that any positive integer is of the form 6q+1 or 6q+3 or 6q+5, where q is some
integer.
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Answer 1

Step-by-step explanation:

Let a is a positive odd integer and apply Euclid’s division algorithm

a = 6q + r, Where 0 ≤ r < 6

for 0 ≤ r < 6 probable remainders are 0, 1, 2, 3, 4 and 5.

a = 6q + 0

or a = 6q + 1

or a = 6q + 2

or a = 6q + 3

or a = 6q + 4

or a = 6q + 5

may be form Where q is quotient and a = odd integer.

This cannot be in the form of 6q, 6q + 2, 6q + 4. [all divides by 2]

Hence, any positive odd integer is of the form 6q + 1, or 6q + 3 or (6q + 5)