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Let p be a prime with p ≡ 3 (mod 4), and suppose that q = 2p + 1 is also prime.

(a) Show that 2 is a square mod q.

(b) Show that 2^p ≡ 1 (mod q), so q | j 2^p - 1. (This explains the fact that 23 | 2¹¹ - 1.)

It is not yet proved that there are infinitely many primes p such that 2p + 1 is prime. It is also not yet proved that there are infinitely many primes p for which M_p is composite.

P = 140 when t = 3 and P = 100 when t = 1

(a) Find values for the parameters k and P0.
(b) State the initial quantity and the continuous percent rate of growth or decay.

Simplify the following expressions by writing each one using a single trigonometric function.

Why do trace gases not accumulate in the troposphere?

Science assignment

Use the chart to complete this assignment

diamond guns germs and steel what is  the ‘economic problem’ and how does tradition works to solve it