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- The positive integer 2011 2012 2013 . . . 2022 2023 has 52 digits. Without changing the order of any of thedigits, any 32 of the digits can be removed. Find the greatest 20-digit number that can be produced in thisway.Which positive integers less than 20 are relatively prime to 20?Is there an integer that has a remainder of 2 when it is divided by 5 and a remainder of 3 when it is divided by 6? a. Is there an integer n such that n has _____?b. Does there exist _________ such that if n is divided by 5 the remainder is 2 and if _____________ ?Note: There are integers with this property. Can you think of one?
- A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds of tortillas, followed by choosing one of 3 different kinds of protein, followed by one of 2 different kinds of cheeses, followed by 1 one 5 different kinds of salsa. How many different integers must be selected to guarantee that at least 5 of them would have the same remainder when divided by 3?Since the next prime after 7 is 11, the smallest composite number whose prime factors are all greater than 7, is ▼ Since this is ▼ less greater than 100, there are no ▼ prime composite numbers, from 2 to 100, whose prime factors are all greater than 7. Therefore, ▼ every at least one composite number from 2 to 100 must be a multiple of some prime number less than or equal to 7.5!, called 5_______ , is the product of all positive integers from_________ down through________ . By definition,0! =_______.
- Suppose that you know that a golfer plays the first hole of a golf course with an infinite number of holes and that if this golfer plays one hole, then the golfer goes on to play the next hole. Prove that this golfer plays every hole on the course.Show that if seven integers are selected from the first 10 positive integers,there must be at least two pairs of these integers with the sum 11.a.) Is the conclusion still true if six integers are selected rather thanseven?Let ab5c be all four-digit multiples of numbers 36 with different digits.If someone found 7 numbers that satisfy that conditions, did he found them all? If no ,can you find them all
- Find the number of positive integers not exceeding 1000 that are not divisible by 2 or 3 butdivisible by 5.Find the set of all positive integers n with the property that the set M={n,n+1,n+2,n+3,n+4,n+5} can be partitioned into two sets such that the product of the numbers in one set equals the product of the numbers in the other set. Please do not give me wrong answer like for n=1 and the sets will be A and B with 3 elements each set, this solution is wrong and the tutor who gave it already to me please do not reply again on this question because you make me lose one question that i have already pay for it, so the answer should respect the above requirements for that problem all of them not only for n=1. Thanks in advance.Compute P7,2. (Enter an exact number.) _________________