Algebra

Advanced Factorization

Factorization of Integers

         

Evaluate (16721652)(16321612)(15921572)166×162×158.\frac{(167 ^2-165 ^2)(163 ^2-161 ^2)(159 ^2-157 ^2)}{166 \times 162 \times 158}.

Evaluate 23×24×25×26+1.\sqrt{23 \times 24 \times 25 \times 26+1}.

\quad What is the real number AA that satisfies

774+772+1772+77+1=782A?\frac{77 ^4+77 ^2+1}{77 ^2+77+1}=78 ^2-A?

What is the value of 490000490000×490001+1490701?490000-\frac{490000 \times 490001+1}{490701}?

If aa, cc and ee are prime numbers such that a<c<ea<c<e and 36+37+38+39=abcdef,3^{6}+3^{7}+3^{8}+3^{9}=a^b c^d e^f, what is the value of bdfbdf?

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