(i) 31000 mod 13
Trigonometric Identities
Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.
Inverse Trigonometric Functions
Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.
For each one of the three powers of modular arithmetic, choose either Fermat’s Little Theorem, Euler’s Theorem, or Euler’s Corollary as appropriate, and calculate its value without computing the actual powers before the modulo. For example, do not first calculate the value of 31000
and then compute its value modulo 13. Make sure to take full benefits of theorem or corollary you pick. If done correctly, you should be able to do this problem without any help of calculators. Clearly identify which theorem or corollary is used and how it is used. Show all work.
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