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N=2x2x2x5x5x7

Find sum of all even divisors of N

What is the sum of all the integers \(a\) such that the following equation has no real roots:

\[\frac{x^2+x+a-5}{x-1}=a?\]

All the 7-digit numbers containing each of the digits 1, 2, 3, 4, 5, 6, 7 exactly once, and not divisible by 5, are arranged in the increasing order. Find ...

√2 + √3 = 3.14 (approximately). Does this have any significance or is it just a coincidence?

Let n!=1x2x3x4x...xn for integer n>=1. If p =1!+(2+2!)+(3+3!)+...+(10+10!), then p+2 when divided by 11! leaves a remainder of?

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