Pythagoren Triples. Sums of Higher Powers and Fermat’s Last Theorem. Divisibility and Greatest Common Divisor. Factorization and Fundamental Theorem of Arithmetic. Congurences, Powers, Fermat’s Little Theorem and Euler’s Formula. Chinese Remainder Theorem. Prime Numbers, Counting Primes. Mersenne Primes and Perfect Numbers. Powers, Roots and Codes. Primality Tests. Euler’s Phi Function and Sums of Divisors. Primitive Roots and Indices. Which Numbers are Sums of Two Squares. Continued Fractions, Square Roots and Pell’s Equation. Generating Functions. Sums of Powers. Cubic curves and Elliptic Curves.

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