Maths Olympiad Daily Problems

For any positive integer n, let τ (n) denote the number of positive divisors of n. If n is a positive integer such that τ(n^2)/τ(n)= 3, compute τ(n^7)/τ(n).

87 is a good qn asks your basics pretty well

Ari repeatedly rolls a standard, fair, six-sided die. Let R(n) be the n th number rolled, and let Q(n) = R(1)· R(2)· . . . · R(n). Let the probability that there exists an n such that Q(n) = 100 and for all m < n, Q(m) is not a perfect square be p/q where p, q are relatively prime positive integers. Find the largest prime factor of p + q.

Happy raksha Bandhan to all MODP community ☺️☺️

Let D be a point on the side AC of triangle ABC. Let E and F be points on the segments BD and BC respectively, such that

😋 Finally I did combi

Is there any one who have allen mock test paper?

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Can anyone tell me answer of this problem?

#beauty 10 marker I guess

A circle having radius r1 centered at point N is tangent to a circle of radius r2 centered at M. Let l and j be the two common external tangent lines to the two circles. A circle centered at P with radius r2 is externally tangent to circle N at the point at which l coincides with circle N, and line k is externally tangent to P and N such that points M, N, and P all lie on the same side of k. For what ratio r1/r2 are j and k parallel?