need help?

Question

can you please solve following congruence:

14x = 5(mod 45)

(where "=" is not the regular equal sign, it represent the congruences)

please show me step by step. I need an example to do my rest of the problems. thank you.

Answer 1

14x=5 mod 45 means that
14x-5=45n, for some n

14x=45n+5=5(9n+1)
for which n's do you have that
14 divides 5(9n+1),
notice that 14=2(7)so
2 has to divide 5(9n+1)
and 7has to divide 5(9n+1)
clearly neither 2 nor 7 divide 5,
so they have to divide 9n+1.
and n=3 works, since 9(3)+1=27+1=28
now
14x=45(3)+5
so x=10

Answer 2

The general method uses "Euclid's Algorithm" to show that the GCD of 14 and 45 is 1, and in parallel the "extended Euclid's Algorithm" to show that 14 * 29 = 1 (mod 45). So we have 14 * (29 * 5) = 5, mod 45, or x = 10. Your book, or a web site, will give a better illustration of the Euclidean Algorithm than a Yahoo! Answer.

Answer 3

OK, 5MOD45 means "If you divide 5 by 45, what's the remainder?". 5/45=0 remainder 5 (forget about fractions, decimals etc.) so 5MOD45=5

So 14x=5MOD45
14x=5

Divide by 14

x=5/14

That is the answer.

NB. Equalities, equivalents and inequalities are all worked out the same way.

Answer 4

Why don't you try and solve it yourself so that you actually learn something and remember it?!