Integers and Divisibility Challenge

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
1 reply · 1K views
anemone
Gold Member
MHB
POTW Director
Messages
3,851
Reaction score
115
Prove that $\dfrac{378^3+392^3+1053^3}{2579}$ is an integer.
 
Mathematics news on Phys.org
Hint:

One can do some algebraic manipulation to the numerator and therefore factorize them.
 

Similar threads

Divisibility Challenge: Find Smallest Integer for $f(x)$
  • lfdahl
  • · Replies 3 ·
  • General Math
Replies
3
High School Probability that 2 distinct integers are divisible by the same number
  • nomadreid
  • · Replies 9 ·
  • Set Theory, Logic, Probability, Statistics
Replies
9
Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
  • anemone
  • · Replies 1 ·
  • General Math
Replies
1
Proving Divisibility by 6 Using Mathematical Induction
  • Monoxdifly
  • · Replies 7 ·
  • General Math
Replies
7
Proof: Divisibility of Integers by 4
  • Math100
  • · Replies 5 ·
  • Precalculus Mathematics Homework Help
Replies
5
Divisibility of Integers ## 176521221 ## & ## 149235678 ## by 9 & 11
  • Math100
  • · Replies 9 ·
  • Precalculus Mathematics Homework Help
Replies
9
How Does Modular Arithmetic Simplify Integer Divisibility Proofs?
  • shamieh
  • · Replies 1 ·
  • General Math
Replies
1
Prove Divisibility of $a^3+b^3+c^3$ Using $(a-b)^2+(b-c)^2+(c-a)^2=abc$
  • anemone
  • · Replies 1 ·
  • General Math
Replies
1
Undergrad The consequence of divisibility definition in integer
  • Seydlitz
  • · Replies 2 ·
  • General Math
Replies
2
Proving Divisibility with the Power of 5
  • anemone
  • · Replies 4 ·
  • General Math
Replies
4