MA2317: Introduction to Number Theory
Tutorial problems, November 27, 2010
√
√
1. Show that 2 + P3 is an algebraic number.
1
2. Show that e =
is irrational. (Hint: e can be approximated
n!
n>0
P 1
=
satisfies
by rational numbers too well: the rational number qpm
n!
m
06n6m
| qpm
m
1
.)
mqm
− e| <
3. Show that the polynomial xn +2(xn−1 +xn−2 +. . .+x)+4 is irreducible
over integers for n > 3.
4. Find a rational parametrisation of the curve y2 + 2x2 − x − y − 1 = 0.