Question

26.
If 15.2*+1 +15.2-*
a)-1
=135, then x is
b) 0
d) 2
c)1

​

Answer 1

Answer:

Step-by-step explanation:

Lemma: If gcd(a,b)=1, then every odd factor of a2 + 3b2 has this same form.

In other words, for every odd factor of a2 + 3b2, there exists c,d such that the odd factor = c2 +3d2

(1) Let x be a positive, odd factor of a2 + 3b2

(2) Then, there exists a value f such that:

a2 + 3b2 = xf

(3) We can assume that x is greater than 1 (since if x = 1 it's only factor is itself and 1 = 12 + 3(0)2.)

(4) There exists integers m,n such that:

a = mx ± c

b = nx ± d

where c,d can be positive or negative.