3

Part of 2015 Albania JBMO TST

Problems(1)

Find the remainder of division of $(m+3)^{1444}$ to $n$

Source: Albania JTST 2015

\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\dots+\frac{1}{2014\cdot2015}=\frac{m}{n},

\frac{m}{n}

is irreducible. a) Find

m+n.

b) Find the remainder of division of

(m+3)^{1444}

n{}