Question

show that any positive odd integer is the form of 6 Cube + 1 or 6 Cube + 3 or 6 Cube + 5 Where Q is some integer​

Answer 1

Ello user !!!!

Here is your answer,

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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.

Therefore,  any positive odd integer is the form of 6 Cube + 1 or 6 Cube + 3 or 6 Cube + 5 Where Q is some integer​

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HOPE THIS HELPS YOUU :)

AND STAY BLESSED.

Answer 2

Answer:Here is your answer