2^125 Mod 127

2^125 Mod 127 -> http://ssurll.com/10axod

f6d3264842 2. Find all primitive roots mod 11. Using #1 and #2 of HW8 with p = 11: 25 ≡ −1 implies .... it follows that 125 is not a square to the modulus 127 (in other words,.. 22 Goal: Modular Exponentiation We need to compute x y mod N for ... the Algorithm 2^125 mod 127 modexp(2,125,127) x=2, y=125, N=127 i=125, r=1, z = 2 .... More simply: mod m=2n−1: 2n≡1⇒2−1≡n≡(m+1)/2 [≡(127+1)/2≡64 ]. Remark The same idea works to compute a−1(modan±1), i.e. when .... The inverse of 17 mod 3120 is 2753 Working out (we are searching for a value of 1) Val (val * n) mod m 1 17 2 34 3 51 4 68 5 85 6 102 7 ... 118 2006 119 2023 120 2040 121 2057 122 2074 123 2091 124 2108 125 2125 126 2142 127 2159 .... Substituting for q, we obtain a""" = b mod (p) (25) where m = [Vp]. We rewrite ... Therefore, for every b, 1 s b = 126, there exists a q, 0 < q = 125, such that 3" = b mod (127). ... 2. We calculate a "= 3" = 85 mod (127). 3. We prepare Tables 6 and 7.. 127 = 2^8 - 1 2^125 = 2^117 * 2^8 = 2^117 * 2^8 - 2^117 + 2^117 = 2^117(2^8 - 1) + 2^117 2^125 mod 127 = 2^117.. How can we calculate A^B mod C quickly if B is a power of 2 ? ... We can substitute our previous result for 7^2 mod 13 into this equation. 7^4 mod 13 = (10 * 10) .... By Fermat's Little Theorem, 2^126 ≡ 1 mod 127. We can write 2^126 = 2^125 * 2. So 2^125 is the inverse of 2 mod 127. By observation (or by extended Euclid's .... 2. Calculate 2^{125} mod 127 using any method you choose. Show your work. Hint: 127 is prime. 3. Compute the GCD of 210 and 588 using Euclid's algorithm.. 18 Jun 2012 ... successive squaring in computing high powers of an integer modulo . ... 2 where ( ) denotes the power set of. , that is, ( ) is the set of all ..... 16. (a) Compute 4126 mod 127. 9 ... 6125 = 53 72 so (6125) = (125 25) (49 7) = 4200.. ... 2125 mod 127 using any method you choose. (Hint: 127 is prime.) ... Calculate 2125 mod 127 using any method you choose. (Hint: 127 is prime.) Step-by-step .... Calculate 2 125 mod 127. Express your answer as the smallest valid non- negative integer. Answer: 2 125 ≡ 2 − 1 2 126 ≡ 2 − 1 ≡ 64 (mod 127) 3.5 (5 points).. The modulo calculator finds the solution of an expression x mod y = r. ... 1 mod 1 = 0 (as mod 1 is always 0); 1 mod 2 = 1; 1 mod 3 = 1; 5 mod 2 = 1; 5 mod 3 = 2 .... 55 = 1 + 2 + 4 + 16 + 32 so 5^55 = 5^1 * 5^2 * 5^4 * 5^16 * 5^32 = 5 * 25 * 625 * 1 * 1 (mod 221) = 125 * 625 (mod 221) = 125 * 183 (mod 183) .... Using Algorithm 7.1, gets k p 1 1 1 · 16 mod 29 = 16 2 16· 16 mod 29 = 24 3 24 · 16 mod 29 = 7 4 7· 16 mod 29 = 25 so 164 mod 29 ... Using Algorithm 7.2, we get 597 mod 127 = 80. ... 125 52000 mod 17 = ( 516 ) mod 17 = 1125 mod 17 = 1 7.. Modular Arithmetic: FLT. Fermat's Little Theorem: a p-1. = 1 mod p, given p is prime. Evaluate 2. 125 mod 127. (hint: 127 is prime) .... 1.25. Calculate 2^125 mod 127 using any method you choose. (Hint: 127 is prime.) Solution: 64 2^125 = 2^119 * 2^6 = 128^17 * 2^6 = 1^17 * 2^6 = 64 Checked .... 1023 = 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = (1111111111)2. Note that ... Because 10 mod 3 = 1, we know 10i mod 3 = 1i mod 3 = 1 for any nonnegative .... 27 − 1 = 127, which is prime b. ..... 232 mod 41 = 125 · 232 mod 41 = 37.. 132- 8 129 2 128-1 125-2 122 9 123-7 127-4 127-2 132-0 135-1 140-8 140-5 ... 4 132- 8 1260 125-5 124-5 122-7 123- 0 123-0 122-9 127- 2 126-2 125-2 135- 1 133- 5 .... Mod. Brisk. Densely overcast ; cirro-strati and haze. 9 0 10 0 Densely .... II. 88 II. 309 Is. 234 I. 659-60 I. 661 I. 682 II. 629 I. 422 II. 576 I. 413 II. 85 II. 415 L. 421 I. 380 I. 57 II. 298 165 524 314 314 315 - 703 117 75 . 635 I. 497 I. 610 I. ... P. W. 504 1 Mod. 127 3 Bac. Ab. Leases, (R.) 3 ... Cred. ii. 125 Tithe, v. 185 Debt.