##### Currency

- USD
- GBP
- AUD
- SGD
- NZD

##### Deadline

- 1 Day
- 2 Days
- 3 Days
- 4-6 Days
- 7-10 Days
- > 10 Days

##### Pages

250 Words

**Question - **Math 324 Assignment 4 (due October 8)
Please remember to staple your assignment and to write the names of other students you
may have worked with.
1. ( 5)(1.5, #46) Show that the nth Fibonacci number fn is divisible by 4 if, and only if,
6 divides n. Hint: Consider the sequence of least residues of fn mod 4.
2. (5)(3.5, #34) Find all pairs of positive integers a, b so that (a, b) = 18 and [a, b] = 504.
3. (6) Determine all solutions x mod 147 of 119x ≡ 98 mod 147.
4. ( 5) Let p be an odd prime and k ≥ 1. What are the solutions mod pk of the congruence
x2 ≡ 1 mod pk ? Prove this.
5. ( 3 + 3)(Continuing Problem 3.7)
a) Show that every non-unit of A can be written as a product of primes of A.
b) Is prime fa
...Read More

**Solution Preview - **starts as 0, 1, 1, 2, 3, 1, 0, 1 for 0 ≤ n ≤ 7, which is long enough
to observe that f n + 6 ≡ f n mod 4 for n = 0, 1, hence for all n ≥ 0 by induction on n:
for n ≥ 2, we have f n + 6 = f n − 1 + 6 + f n − 2 + 6 ≡ f n − 1 + f n − 2 = f n mod 4. For 0 ≤ r < 6,
another induction, started by the one above, gives f 6q + r ≡

**Original Question Documents**

Email your assignment/project

Want to place an

order on the call?**It's free**

order on the call?