MathDB

2:

Part of 1994 Romania TST for IMO

Problems(3)

Divisible by $((n-1)^n+1)^2$ (Romania TST 1994)

Source: Romania TST 1994

8/4/2009
Let n n be an odd positive integer. Prove that ((n−1)n+1)2((n-1)^n+1)^2 divides n(n−1)(n−1)n+1+n n(n-1)^{(n-1)^n+1}+n.
modular arithmeticnumber theory proposednumber theory
romania tsts

Source: Romania TST for IMO 1994 second exam

9/6/2017
Let S1,S2,S3S_1, S_2,S_3 be spheres of radii a,b,ca, b, c respectively whose centers lie on a line ll. Sphere S2S_2 is externally tangent to S1S_1 and S3S_3, whereas S1S_1 and S3S_3 have no common points. A straight line t touches each of the spheres, Find the sine of the angle between ll and tt
geometry
romania tst

Source: Romania TST for IMO 1994,third test

9/6/2017
Let nn be a positive integer. Find the number of polynomials P(x)P(x) with coefficients in {0,1,2,3}\{0, 1, 2, 3\} for which P(2)=nP(2) = n.
algebra