Subcontests
(5)a_i + j = n + 1 where i = a_j, permutations of 1,2,...,n , when 4 divides n
Let n be a positive integer divisible by 4. We consider the permutations (a1,a2,...,an) of (1,2,...,n) having the following property: for each j we have ai+j=n+1 where i=aj . Prove that there are exactly (41n)!(21n)! such permutations. angle chasing candidate, right angle wanted, equal angles given
Let △ABC be a triangle. The angle bisector of ∠CAB intersectsBC at L. On the interior of line segments AC and AB, two points, M and N, respectively, are chosen in such a way that the lines AL,BM and CN are concurrent, and such that ∠AMN=∠ALB. Prove that ∠NML=90o. prime power criterion with a @ b = \frac{a - b}{gcd(a, b)}
For all positive integers a and b, we dene a@b=gcd(a,b)a−b .
Show that for every integer n>1, the following holds:
n is a prime power if and only if for all positive integers m such that m<n, it holds that gcd(n,n@m)=1.