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Solution :

`a = 3q + r` <br>
(Euclid's) `3 lt r le 0 or 1 or 2 ` <br>
`a = 3q or 3q+1 or 3q+2` <br>
`a^2 = (3q)^2 or (3q + 1)^2 or (3q+2)^2` <br>
`= 9q^2 or 9q^2+6q+1 or 9q^2+12q+4` <br>
`= 3(3q^2)or 3(3q^2 + 2q)+1 or 3(3q^2+ 4q+1)+1` <br>
let `(3q^2) & (3q^2 + 2q) & (3q^2+ 4q+1)` be m , n and p respectively <br>
`a^2 = 3m or 3n+1 or 3p+1` <br>
`a^2 = 3m or 3m+1`<br>
this will satisfy every value of a <br>
hence proved**Review of previous class**

**Divisibility**

**Properties of Divisibility**

**What is Euclid Division ?**

**Euclid Division lemma**

**Proof of Euclid division lemma**

**Prove that one of every three consecutive positive integers is divisible by 3.**

**Euclid division algorithm**

**HCF of two positive integers
**

**Use Euclid's division algorithm to find the HCFof 210 and 55.**