[tex]22. \: \: \frac{a}{2} = \frac{b}{3} [/tex]
[tex]a \times 3 = 2 \times b[/tex]
[tex](14 a - 21b + 1)^{2013} = 1[/tex]
[tex](14a - 7 \times 3b + 1)^{2013} = 1[/tex]
[tex](14a - 14a + 1)^{2013} = 1[/tex]
[tex](0 + 1)^{2013} = 1[/tex]
[tex]{1}^{2013} = 1[/tex]
[tex]23. \: \: \frac{a}{2} = \frac{b}{3} = \frac{c}{5} = k[/tex]
[tex]a = 2k \\ b = 3k \\ c = 5k[/tex]
[tex](a + b - c)^{2013} = 1[/tex]
[tex](2k + 3k - 5k)^{2013} = 1[/tex]
[tex] {0}^{2013} = 1[/tex]