Limited-Time Offer (50% Off Forever) - Start Your Membership Today! (Monthly) (Yearly)

Ran

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q7 Members Public

Establish the following divisibility criteria: (a) An integer is divisible by 2 if and only if its units digit is 0,2,4,6, or 8. (b) An integer is divisible by 3 if and only if the sum of its digits is divisible by 3. (c) An integer is divisible by 4 if and only if the number...

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q6 Members Public

My Solution for "Working modulo 9 or 11, find the missing digits in the calculations below: (a) 51840273581=1418243x040. (b) 2x99561=[3(523+x)]2. (c) 2784x=x5569. (d) 5121x53125=1000000000."

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q5 Members Public

My Solution for "(a) Obtain the following generalization of Theorem 4.6: If the integer N is represented in the base b by N=ambm++a2b2+a1b+a00akb1N = a_{m}b^{m} + \cdots + a_{2}b^{2} + a_{1}b + a_{0} \qquad 0 \leq a_{k} \leq b - 1 then b1N if and only if ..."

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q4 Members Public

My Solution for "Without performing the divisions, determine whether the integers 176521221 and 149235678 are divisible by 9 or 11."

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q3 Members Public

My Solution for "Find the last two digits of the number 999. [Hint: 999(mod10); hence, 999=99+10k; notice that 9989(mod100).]"

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q2 Members Public

My solution for "Prove the following statements: (a) For any integer a, the units digit of a2 is 0,1,4,5,6, or 9. (b) Any one of the integers 0,1,2,3,4,5,6,7,8,9 can occur as the units digit of a3. (c) For any integer a, the units digit of a4 is 0,1,... "

Ran
Ran
Math

Elementary Number Theory Problems 4.3 Solution (David M. Burton's 7th Edition) - Q1 Members Public

My Solution for "Use the binary exponentiation algorithm to compute both 1953(mod503) and 14147(mod1537). "

Ran
Ran
Math

Basic Techniques for Solving Theory of Congruence Problems - 1 Members Public

8 Basic Techniques for solving theory of congruence/Modular Arithmetic problems summarised from my solution on Chapter 4.2 Elementary Number Theory 7th Edition Problems (David M. Burton).

Ran
Ran
Math