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			Prove:::::::: If gcd(a,n)=1,then the integers c,c+a,c+2a,c+3a,...........................,c+(n-1)a form a complete set of reidues modulo n, for any c. ... 
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			*Prove that every integer of the form n^4+4 is always composite......... ... 
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			Prove that any integer of the form 3k+2 also has a prime factor of the form 3k+2............ ... 
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			1)Can I appear for GATE after doing BSc in Mathematics.? 2)If I take up B.Tech Eng. then,I can give GATE in 3rd or 4th year? ... 
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			Prove if gcd(a,b)=1,then gcd(a^2,b^2)=1. ... 
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			1.Prove that 24 divides 2.7^n+3.5^n-5.(n>=1) 2.Prove that the sum of the squares of two odd integers cannot be a perfect square. 3.If there exists x and y for which ax+by=gcd(a,b),then gcd(x,y)=1.(a,b are integers) 4.Prove ... 
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			1)There are seven people in a elevator.The lift stops at 3(unspecified) floors.In each stop or more people get out, but no one boards it.After 3 stops it is found that the elevator is empty.Find the no. of way this can happen ... 
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