Respuestas
(n+1)*(4+1) = 35
n+1(5) = 35
n+1 = 7
n = 6
Explicacion
(n+1)*(4+1) = 35
n+1(5) = 35
n+1 = 7
n = 6
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10)
nos dicen que  tiene 24 divisores.
primero reducimos...




ahora que las bases son números primero podemos continuar...
(2 +  + 1)( +1) = 24
( + 3)( +1) = 24
² + 4 + 3 = 24
² + 4 = 21
 = 3
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11)
nos dicen que M = 12 * 15ⁿ, tiene 60 divisores, la misma técnica, reducimos...
M = 3 * 4 * (3*5)ⁿ
M = 3 * 2² * 3ⁿ * 5ⁿ
M = 2² * 3¹ * 3ⁿ * 5ⁿ
M = 2² * 3¹⁺ⁿ * 5ⁿ
ahora, seguimos:
(2+1)(n+2)(n+1) = 60
3(n+2)(n+1) = 60
n²+3n+2 = 20
n²+3n = 18
n = 3
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12)
N = 6 * 8ˣ; tiene 16 divisores.
N = 2 * 3 * (2³)ˣ
N = 2 * 2³ˣ * 3
N = 2¹⁺³ˣ * 3
...
(3x+2)(2) = 16
(3x+2) = 8
3x = 6
x = 2
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13)
M = 77 * 9ⁿ; tiene 60 divisores.
M = 7 * 11 * (3²)ⁿ
M = 7 * 11 * 3²ⁿ
(2)(2)(2n+1) = 60
(2n+1) = 15
2n = 14
n = 7