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a^2=b^2(mod n) need not imply a=b(mod n)
(b) Prove that n is an odd pseudoprime number if and only if 2"-1-1 mod n.
(b) Prove that n is an odd pseudoprime number if and only if 2"-1-1 mod n.
I have first part of question good. Need to prove unique modulo
and do not know where to start.
Prove that the congruences x-a mod n and x b mod m admit a simultaneous solution if and only if (n, m) | (a -b). Moreover, if a solution exists, then the solution is unique modulo [m, n).
Prove that the congruences x-a mod n and x b mod m admit a simultaneous solution if and only if (n, m) |...
Prove that transitivity implies each of the following claims: . If a ~ b andb ~~ c, then a c. bc, then da (Harder) If a - bandb~c, then a c. In each case, first convert the strict/indifferent statement to an equivalent statement using only weak preference. Then prove the equivalent statement using our definition of transitivity, which involves only weak preference.
Recall that: ged: NN → N gcd(a,0) = a. gcd(a,b) = gcd(b, mod(a,b)), if b > 0. and mod : Nx (N – {0}) ► N mod(a,b) = a if a <b. mod(a,b) = mod(a - b,b), if a > b. and fib: N → N fib(0) = 0 fib(1) = 1 fib(n) | if n >1=fib(n − 1) +fib(n - 2) Prove the following by induction. you cannot use any extra lemmas or existing results. Vn e N, ged(fib(n...
comute the following
(a) 55555555 mod 5555 (b) 77766 mod 5 (c) Let n be a composite integer bigger than 4, compute n-1 i mod n i=1
Suppose a
c mod n and bd
mod n.
(a) show that a + b
c + d mod n
(b) show that a * b
c * d mod n.
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2. Let a,b,c E Z. Prove the following. If aſb then g.c.d(b, c) = 1 implies g.c.d(a, c) = 1.
If m and n are coprime positive integers, prove that φ(n) no(m)-1 (mod mn).