Cbse grade 10 magic problems a challenge for evey one

Number Theory Level pending

1)If a an b are positive integers then we know that a=bq+r,0<=r<b....where q is a whole number,prove that HCF(a,b)=HCF(b,r)

2)Prove by contradiction- If a^2 is even then a is also even If a^2 is divisible by 3 then a is also divisible by 3 Show that there is no value for n for which 6^n ends with 0 R is a rational number and X is a irrational number then prove that R+X is a irrational number

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