Well, first consider how many digits there are. You have 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, depending on how you use it, that are all digits. If you count 0 as a digit other than a place holder (0000, 0001, etc.), you would end up with ten thousand (10,000) numbers with four digits, starting with 0000, and ending with 9999. If you count 0 as nothing other than a place holder (1000, 1001, etc.), you would have nine thousand (9,000) numbers with four digits, starting with 1000. So, depending on how you view 0, you can make up to 10,000 different numbers that contain four digits.
(Hard) A composite number n is called a Carmichael number bn−1 ≡ 1 (mod n) for every number b such ... Base case: When n = 2 the formula a + c ≡ b + d (mod m) was already given. ... The sequence goes 1, 3, 7, 15, 31,... guess that it is equal to 2n+1 − 1. ... Prove (now using induction on n) that fm|fmn for all n ≥ 1.
Let’s take x as the price of a taco and y as the price of a serving of nachos. 22x + 17y = 71.05. First order 10x + 5y = 27.25. Second order Multiply the first order by 5 and the second order by 11 110x + 85y = 355.25 110x + 55y = 299.75 Subtract 30y = 55.5 y = 1.85 So 10x + 5x1.85 = 27.25 10x = 27.25 - 9.25 = 18 x = 1.8
So each taco cost $1.80 and an order of nachos cost $1.85