# Mock AIME 1 2010 Problems/Problem 1

Revision as of 18:42, 12 March 2010 by Kevin Zhang (talk | contribs) (Created page with 'Since <math>n^2 = 7k+4</math>, <math>n^2</math> is congruent to <math>4</math> mod <math>7</math>. Taking the square root of both sides, we obtain <math>n</math> is congruent to…')

Since , is congruent to mod . Taking the square root of both sides, we obtain is congruent to mod . Solving, is congruent to either or mod . The maximum of is , of which the square root is between and . So, must be less than . The series of solutions for is and . However, does not work because , a value not possible for . Thus, there are different solutions for a total of solutions.