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Consider the number
N=123456789101112…9899100‾, N = \overline{123456789101112\ldots 9899100}, N=123456789101112…9899100,
which is obtained from writing all the integers from 1 to 100 and removing the spaces that are in between. What are the first 3 digits of N2N^2 N2?
Evaluate
⌊(23+17)4⌋. \lfloor \left( \sqrt{ 23 } + \sqrt{17 } \right)^4 \rfloor . ⌊(23+17)4⌋.
If the quartic x4+9x3+11x2+36x+A x^4 + 9x^3 + 11 x^2 + 36 x + A x4+9x3+11x2+36x+A has roots k,l,m k, l, mk,l,m and nn n such that kl=mnkl = mn kl=mn, determine AAA.
Integers NNN and MMM satisfy 0≤M≤21! 0 \leq M \leq 21! 0≤M≤21! and
∑i=121(i2+i+1)i!=N×21!−M. \sum_{i=1}^{21} (i^2 + i + 1) i ! = N \times 21 ! - M. i=1∑21(i2+i+1)i!=N×21!−M.
What is N+MN + M N+M?
If x=11+7 x = \sqrt{ 11 + \sqrt{ 7 } } x=11+7 and y=11−7 y = \sqrt{ 11 - \sqrt{ 7 } } y=11−7, evaluate
x6+y6. x^6 + y^6. x6+y6.
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