- Euclid's Theorem
and Its consequence
- If a, b belongs to Z then show that
- If a/b and b/a this implies a =
±b.
- If a/b and b/c then a/c.
- If a/b then a/bc.
- If a/b then ac/bc.
- If a/b and a/c then a/bx+cy for x,y belongs
to Z.
- If a/b1+b2 and a/b1 then a/b2.
- a/o
- 1/a
- Show that (a-b)/(an -bn) for all n greater than and equal to Zero and belongs to Z.
- Prove that if n is an odd integer then 8/n^2 -1.
- Prove that product of three consecutive integers is divisible by 6
- Prove that (a+b)/(an - bn) , if n is a positive even integer.
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