5

Part of 2020 LIMIT Category 1

Problems(2)

Source: LIMIT 2020

P(x),Q(x)

be monic polynomials with integer coeeficients. Let

a_n=n!+n

for all natural numbers

n

\frac{P(a_n)}{Q(a_n)}

is an integer for all positive integer

n

\frac{P(n)}{Q(n)}

is an integer for every integer

n\neq0

. \\ Hint (given in question): Try applying division algorithm for polynomials

algebrapolynomialalgorithm

Intersection of lines

Source: LIMIT 2020 Cat 1 Obj P5

Rohit is counting the minimum number of lines

m

, that can be drawn so that the number of distinct points of intersection exceeds

2020

m

63

64

65

66