Recall that a permutation of {1, 2,..., n} is a one-to-one correspondence P from the set {1, 2, ..., n} to itself (or a 'rearrangement' of 1, 2,..., n). For example, P(1) = 3, P(2) = 2, P(3) = 1 defines a permutation of {1, 2,3}. Let N be an integers whose digits are 12 ... 4591. (For example, the number 415 has digits x₁ = 4, x₂ = 1, x3 = 5.). If P is a permutation of {1, 2, ..., 4591}, what is the largest integer k that is guaranteed to divide the difference x1x2x4,591 P(1)*P(2) .P(4591) for any possible value of N and any permutation P. (Hint: consider the sum of the digits of the numbers in question.)
Recall that a permutation of {1, 2,..., n} is a one-to-one correspondence P from the set {1, 2, ..., n} to itself (or a 'rearrangement' of 1, 2,..., n). For example, P(1) = 3, P(2) = 2, P(3) = 1 defines a permutation of {1, 2,3}. Let N be an integers whose digits are 12 ... 4591. (For example, the number 415 has digits x₁ = 4, x₂ = 1, x3 = 5.). If P is a permutation of {1, 2, ..., 4591}, what is the largest integer k that is guaranteed to divide the difference x1x2x4,591 P(1)*P(2) .P(4591) for any possible value of N and any permutation P. (Hint: consider the sum of the digits of the numbers in question.)
A First Course in Probability (10th Edition)
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Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Need help with this difficult Intro to Elementary Number Theory Homework problem.
![Recall that a permutation of {1, 2,..., n} is a one-to-one correspondence P from the set {1,2,...,n} to itself (or a 'rearrangement' of 1, 2, ..., n). For example,
P(1) = 3, P(2) = 2, P(3) = 1
defines a permutation of {1, 2, 3}.
Let N be an integers whose digits are X₁ X2 ... 4591. (For example, the number 415 has digits x1 = 4, x2 = 1, x3 = 5.). If P is a permutation of {1, 2, ..., 4591}, what is
the largest integer k that is guaranteed to divide the difference
X1 X2 X4,591 XP(1) P(2) Xp(4591)
for any possible value of N and any permutation P. (Hint: consider the sum of the digits of the numbers in question.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F988321fe-2fa3-453d-a72b-be5ece348fb5%2F44c2db8f-3d99-4d84-881b-c3da89c12d21%2Ffa0bcrx_processed.png&w=3840&q=75)
Transcribed Image Text:Recall that a permutation of {1, 2,..., n} is a one-to-one correspondence P from the set {1,2,...,n} to itself (or a 'rearrangement' of 1, 2, ..., n). For example,
P(1) = 3, P(2) = 2, P(3) = 1
defines a permutation of {1, 2, 3}.
Let N be an integers whose digits are X₁ X2 ... 4591. (For example, the number 415 has digits x1 = 4, x2 = 1, x3 = 5.). If P is a permutation of {1, 2, ..., 4591}, what is
the largest integer k that is guaranteed to divide the difference
X1 X2 X4,591 XP(1) P(2) Xp(4591)
for any possible value of N and any permutation P. (Hint: consider the sum of the digits of the numbers in question.)
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