3

Part of 2007 Postal Coaching

Problems(2)

if 4^n + 2^n + 1 is a prime then n = 3^k

Source: Indian Postal Coaching 2007 set 3 p3

n

is a natural number such that

4^n + 2^n + 1

is a prime. Prove that

n = 3^k

for some nonnegative integer

k

power of 3number theoryprime

a^{2007} = a + 1 and b^{4014} = b + 3a

Source: Indian Postal Coaching 2007 set 6 p3

a

b

be two positive real numbers such that

a^{2007} = a + 1

b^{4014} = b + 3a

. Determine whether

a > b

b > a

algebrainequalities