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Exercise 0 (8.3 (b),(c),(d),(e)).
Find all incongruent solutions to each of the following congruences:
(b)
(c)
(d)
(e)
Question 1 (12.2 (a)).
Show that there are infinitely many primes of the for 6n+5.
Exercise 2.
Determine the value of
Question 3.
Show that the equation
has no nonzero integer solutions.
Does it have nonzero solutions mod 6?
Question 4 (based on 2.1 (b)).
Show that in a primitive Pythagorean triple a,b,c exactly one of a,b,c is divisible by 5.
Question 5 (8.4 (d))
Show that a number is divisible by 9 if and only if its sum of digits is divisible by 9.
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Find all incongruent solutions to each of the following congruences:
(b)
(c)
(d)
(e)
Question 1 (12.2 (a)).
Show that there are infinitely many primes of the for 6n+5.
Exercise 2.
Determine the value of
Question 3.
Show that the equation
has no nonzero integer solutions.
Does it have nonzero solutions mod 6?
Question 4 (based on 2.1 (b)).
Show that in a primitive Pythagorean triple a,b,c exactly one of a,b,c is divisible by 5.
Question 5 (8.4 (d))
Show that a number is divisible by 9 if and only if its sum of digits is divisible by 9.