Algebra

Advanced Factorization

Algebraic Manipulation

         

Consider the number

N=1234567891011129899100, N = \overline{123456789101112\ldots 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 ?

Evaluate

(23+17)4. \lfloor \left( \sqrt{ 23 } + \sqrt{17 } \right)^4 \rfloor .

If the quartic x4+9x3+11x2+36x+A x^4 + 9x^3 + 11 x^2 + 36 x + A has roots k,l,m k, l, m and nn such that kl=mnkl = mn , determine AA.

Integers NN and MM satisfy 0M21! 0 \leq M \leq 21! and

i=121(i2+i+1)i!=N×21!M. \sum_{i=1}^{21} (i^2 + i + 1) i ! = N \times 21 ! - M.

What is N+MN + M ?

If x=11+7 x = \sqrt{ 11 + \sqrt{ 7 } } and y=117 y = \sqrt{ 11 - \sqrt{ 7 } } , evaluate

x6+y6. x^6 + y^6.

×

Problem Loading...

Note Loading...

Set Loading...