2. Show that any positive odd integer is of the form 6q+1, or 6q +3, or 64 +5, where q is
some integer​

1 thought on “2. Show that any positive odd integer is of the form 6q+1, or 6q +3, or 64 +5, where q is<br />some integer​”

1. Answer:

   Answer: According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b.

   Let a be a given integer.

   On dividing a by 6 , we get q as the quotient and r as the remainder such that

   a = 6q + r, r = 0,1,2,3,4,5

   when r=0

   a = 6q,even no

   when r=1

   a = 6q + 1, odd no

   when r=2

   a = 6q + 2, even no

   when r = 3

   a=6q + 3,odd no

   when r=4

   a=6q + 4,even no

   when r=5,

   a= 6q + 5 , odd no

   Any positive odd integer is of the form 6q+1,6q+3 or 6q+5

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