Question

Which of the following congruences have solutions?

a) x^{2} Congruent 7(mod 53)

b) x^{2} Congruent 14(mod 31)

c) x^{2} Congruent 53(mod 7)

d) x^{2} Congruent 25(mod 997)

All of them please!!

Answer #1

Find all solutions to the following sets of simultaneous
congruences
(a) x ≡ 10 mod 27 and x ≡ 172 mod 243
(b) x ≡ 10 mod 27 and x ≡ 172 mod 243 and x ≡ 163 mod 225
(c) x ≡ 10 mod 27 and x ≡ 172 mod 243 and x ≡ 162 mod 225

Find the solution the solutions of the following congruences
a.13x \equiv 20 (mod 33)
b.116x \equiv 41(mod 160)

7. a. Verify the following congruences: 105 ≡ 5 (mod 20) 189 ≡ 9
(mod 15) b. Verify that ( 105 + 30 ) ≡ ( 5 + 10 ) (mod 20) c. Try
to show that in general, if M≡a (mod L) and N≡b (mod L) then
M+N≡a+b (mod L)

Find all solutions to each congruence.
(a) 2x − 3 ≡ 2 (mod 7)
(b) 3x + 4 ≡ 1 (mod 5)
(c) 3x ≡ 6 (mod 9)
(d) 14x ≡ 11 (mod 15)

find the following square roots.
A. √8( mod 41)
B. √7(mod 41)
C. √7 (mod 19)
D. √7 (mod 29)
E. √5 (mod 29)

For each of the following congruences if there is a solution,
express the solution in the form x
≡ some_number (mod
some_modulus), e.g. x ≡ 6 (mod 9). To standardize
answers, some_number should always be a value
in the range {0, 1, 2, ..., some_modulus -1}. For example
x ≡ 5 (mod 8) is OK but x ≡ 13 (mod 8) is not.
If there is no solution say "No solution". You don't have to
show work for any of the problems. Type...

(7) Which of the following statement is TRUE?
(A) If am−1 ≡ 1 (mod m), then by Fermat’s Little Theorem m must
be a prime.
(B) If ac ≡ bc (mod m), then a ≡ b (mod m).
(C) If a ≡ b (mod m) and n | m, then a ≡ b (mod n).
(D) If 2n −1 is a prime, then 2n−2(2n −1) is a perfect
number.
(E) If p is a prime, then 2p −1 is also...

Determine whether the following integers are congruent to 3
modulo 7:
(a) 37
(b) 66
(c) -17
(d) -67
(e) 80

Which of the following solutions will have the lowest freezing
point? a.) KF (aq) 0.50m b.) glucose soln (0.60m) c.) sucrose soln
(0.60m) d.)FeI3 (aq) (0.24 m)
If you could PLEASE EXPLAIN that would be great! Thank you

Which of the following solutions would have the largest percent
ionization? Assume that they 5) are all 0.10 M in acid at 25∘C. The
acid is followed by its Ka value.
A) HNO2, 4.6 × 10^-4
B) HClO2, 1.1 × 10-2
C) HCHO2, 1.8 × 10^-4
D) HF, 3.5 × 10^-4
E) HCN, 4.9 × 10^-10
Corrent answr is B but WHY?

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