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Curriculum · Number Theory · Diophantine Equations

Diophantine Equations

Integer-solution hunting: factoring tricks, bounding, and Simon's Favorite Factoring Trick.

Objectives

  • Factor to force integer constraints
  • Bound solutions before searching
  • Apply SFFT

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Diophantine Equations mastery now.

Train the topic

●●●○○How many ordered pairs of positive integers (x,y)(x, y) satisfy xy+3x+2y=30xy + 3x + 2y = 30?AIME style●●●○○How many ordered pairs of positive integers (x,y)(x, y) satisfy 3x+5y=473x + 5y = 47?AMC 10 style●●●●○How many ordered pairs of positive integers (x,y)(x, y) satisfy x2−y2=45x^2 - y^2 = 45?AIME style