Number Theory ( Level 3 or 4 maybe )
Number Theory
Level
2
Which of the following values of x will satisfy the equation
3k > E = f2(k) + f3(k) + f4(k) + f5(k) ............fx(k) > 2.25k ?
Here fp(k) is Legendre's function or rather if p,k are naturals, then fp(k) = Highest power of p dividing k!.
5
100
All of these
10
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1 solution
Use the fact that fp(k) is greater than or equal to k/p, when p is a prime.