Tag Archives: Number Theory

[Soln] 2013 AIME I Problem 15

2013 AIME I 15. Let  be the number of ordered triples  of integers satisfying the conditions (a) , (b) there exist integers , , and , and prime where , (c) divides , , and , and (d) each ordered triple … Continue reading

2013 AIME I Problem 15

2013 AIME I 15. Let  be the number of ordered triples  of integers satisfying the conditions (a) , (b) there exist integers , , and , and prime where , (c) divides , , and , and (d) each ordered triple … Continue reading

[Soln] 2013 AIME I Problem 11

2013 AIME I 11. Ms. Math’s kindergarten class has 16 registered students. The classroom has a very large number, , of play blocks which satisfies the conditions: (a) If 16, 15, or 14 students are present, then in each case all the blocks … Continue reading

2013 AIME I Problem 11

2013 AIME I 11. Ms. Math’s kindergarten class has 16 registered students. The classroom has a very large number, , of play blocks which satisfies the conditions: (a) If 16, 15, or 14 students are present, then in each case all the blocks … Continue reading

[Soln] 2016 Pan-African Math Olympiad Problem 3

2016 PAMO 3. For any positive integer , we define the integer as Find the greatest common divisor of the integers .