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    Solve for trig equation with 2 variables

    Homework Statement Homework Equations The Attempt at a Solution I can solve the first part of the question. -2 ≤ k ≤ 2 because -1 ≤ sin(x) ≤ 1. How do I solve the second part of the question? Thanks.
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    Lower Bound of Sequence

    Homework Statement Homework Equations The Attempt at a Solution This is what I have so far: x_{n+1}=\frac{x^5_n + 1}{5x_n}=1 x_{n+2}=\frac{x^5_{n+1} + 1}{5x_{n+1}}=\frac{1^5+1}{5} I think you have to do some sort of repeated substitution but I don't quite see it. Any help? Thanks.
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    Find positive integers a,b,n that satisfy this expression

    Homework Statement Are there any positive integers n, a and b such that 96n+88=a^2+b^2 Homework Equations The Attempt at a Solution It resembles the Pythagorean theorem but I'm not sure how that would help me solve it. I factored the LHS 2^3((2^2)(3)n+11)=a^2+b^2 How do I...
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    Prove this is divisible by 228 for any n

    Homework Statement Prove that the following is divisible by 228 for any n (natural number). 1561^n + 712^n -1225^n - 364^n Homework Equations The Attempt at a Solution I'm guessing you have to prove by induction. When n = 1, the quotient is 3. What do I do afterwards? Thanks.
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