• Euclid’s Algorithm
• Extended Euclidean Algorithm
• State and Prove the Fundamental Theorem of Arithmetic
• Prove that there are infinite primes. Estimate how many primes in between 1 to N.
• Find the upper bound of
  $\epsilon_p(n!).$ And find the formula for $\epsilon_2(n!).$
• Exercise:
  • Prove that $gcd(km, kn) = k\cdot gcd(m, n)$
  • Express $\epsilon_p(n!)$ in terms of $v_p(n)$, the sum of digits of n in base p representation
  • Prove that, $gcd(12n+1, 30n+2)=1$.