More PreRMO or PRMO practice questions 2019

  1. Find the remainder when 37^{100} is divided by 29.
  2. Compute the last two digits of 9^{1500}.
  3. Prove for any integers a and b that a^{2}+b^{2} never leaves a remainder of 3 when divided by 4.
  4. Prove that the equation a^{2}+b^{3}=3c^{2} has no solutions in non zero integers a, b and c.
  5. Prove that the square of any odd integer always leaves a remainder of 1 when divided by 8.

More later,

Nalin Pithwa


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