rM(11) 196and 38220(iii) 867 and2552/Show that any positive odd intege

1.	rM(11) 196and 38220(iii) 867 and2552/Show that any positive odd integer is ofthe form 6g-l, or 6q+3, or 64 + 5, where g issome integer
Answer» 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 lemmaa=bq+ra=6q+rwhere , a=0,1,2,3,4,5then,a=6qora=6q+1ora=6q+2ora=6q+3ora=6q+4ora=6q+5 but here,a=6q+1 & a=6q+3 & a=6q+5 are odd.

rM(11) 196and 38220(iii) 867 and2552/Show that any positive odd integer is ofthe form 6g-l, or 6q+3, or 64 + 5, where g issome integer

Answer»

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 lemmaa=bq+ra=6q+rwhere , a=0,1,2,3,4,5then,a=6qora=6q+1ora=6q+2ora=6q+3ora=6q+4ora=6q+5

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