Question

Usedivision algorithm to show that any positive odd integer is of the form 69 +1,
or 64 +3 or 6q+5, where q is some integer.​

Answer 1

Step-by-step explanation:

Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5; where q is some integer. Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder. but here, a=6q+1 & a=6q+3 & a=6q+5 are odd.

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Answer 2

Answer:

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Show That Any Positive Odd Integer Is Of The Form 6q 1 Or 6q 3 Or 6q 5 Where Q Is Some Integer



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

Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder.

according to Euclid’s division lemma

a=bq+r

a=6q+r

where , a=0,1,2,3,4,5

then,

a=6q

or

a=6q+1

or

a=6q+2

or

a=6q+3

or

a=6q+4

or

a=6q+5

but here,

a=6q+1 & a=6q+3 & a=6q+5 are odd.

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