Junior High Maths

Wednesday, 25 January 2017

Problem 25

Show that 43ⁿ + 83 x 92^3n-1 is divisible by 7 for all positive integers n.

Posted by Từ Nguyên Học at 17:57

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Labels: divisibility, number theory, whole number

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arithmetic (1) arithmetic sequence (2) biprime (1) calculus (1) Cartesian product (1) Chinese remainder theorem (2) composite number (1) cyclic quadrilateral (1) divisibility (6) elementary algebra (14) Euclid's formula (1) Euclidian geometry (6) Euler's phi function (1) Euler's totient function (1) Euler's totient theorem (1) exponentiation (1) Fermat–Euler theorem (1) Fermat's little theorem (2) function of one variable (1) functional equation (1) fundamental theorem of arithmetic (2) geometric sequence (1) Gregorian calendar (1) Hero's formula (1) Heron's formula (1) Heronian triangle (1) induction (9) irrational number (1) isoceles triangle (1) linear congruence equation (4) linear Diophantine equation (2) linear function (1) number theory (11) perfect square (1) polynomial factorisation (3) prime number (3) Ptolemy's theorem (1) Pythagoras' theorem (1) Pythagorean triple (4) reductio ad absurdum (4) semiprime (1) set theory (1) square root (2) summation (4) unique factorization theorem (3) unique-prime-factorization theorem (3) whole number (16)

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▼ 2017 (31)
- ▼ January (31)
  - Problem 31
  - Problem 30
  - Problem 29
  - Problem 28
  - Problem 27
  - Problem 26
  - Problem 25
  - Problem 24
  - Problem 23
  - Problem 22
  - Problem 21
  - Problem 20
  - Problem 19
  - Problem 18
  - Problem 17
  - Problem 16
  - Problem 15
  - Problem 14
  - Problem 13
  - Problem 12
  - Problem 11
  - Problem 10
  - Problem 9
  - Problem 8
  - Problem 7
  - Problem 6
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  - Problem 1

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