Question

if b is integer integer and a non integer then there exist q and r integers such that b=aq+r where 0​

Answer 1

Answer:

Letaandbareintegers,b>0

LetusconsidertheA.Pwithfirst

termaandcommondifferenceb.

Thentheseriesis−

−−−−,(a−3b),(a−2b),(a−b),a,(a+b),(a+2b),−−−−

Letrbethesmallesttermsatisfyingtheinequality

0<r<b.Thenwecanhaveanonintegerqsuchthat

a−bq=r

⇒a=bq+r−−−−0<r<b

∴OptionCiscorrect.