Understand the problem Let (g : mathbb{N} to mathbb{N} ) with ( g(n) ) being the product of digits of (n). (a) Prove that ( g(n)le n) for all ( n in mathbb{N} ) . (b) Find all (n in mathbb{N} ) , for which ( n^2-12n+36=g(n) ). Source of the problem...

Understand the problem Let (p_1,p_2,p_3) be primes with (p_2neq p_3), such that (4+p_1p_2) and (4+p_1p_3) are perfect squares. Find all possible values of (p_1,p_2,p_3). Start with hints Hint 0Hint 1Hint 2Hint 3Hint 4 Do you really need a hint? Try it first!...

Understand the problem For all natural numbers(n), let (A_n=sqrt{2-sqrt{2+sqrt{2+cdots +sqrt{2}}}}) (( n) many radicals) (a) Show that for (nge 2, A_n=2sin frac{π}{2^{n+1}}). (b) Hence, or otherwise, evaluate the limit ...

Understand the problem Suppose that (PQ) and (RS) are two chords of a circle intersecting at a point (O) , It is given that (PO=3) cm and ( SO=4) cm . Moreover, the area of the triangle (POR) is (7 cm^2 ) . Find the are of the triangle (QOS) . Source of the problem...