# Tag Archives: Number Theory

## p^2-q and q^2-p prime

“ and  are 2 prime numbers.  and  are also prime. If you divide  by a composite number , where , you’ll get a remainder of 14. If you divide  by the same number, what will you get as the remainder?” – Akash Advertisements

## [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