Junior High Maths

Showing posts with label Chinese remainder theorem. Show all posts

Showing posts with label Chinese remainder theorem. Show all posts

Friday, 20 January 2017

Problem 20

Find the last digit of 43⁴³.

Posted by Từ Nguyên Học at 16:55 No comments:

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Labels: Chinese remainder theorem, Euler's phi function, Euler's totient function, Euler's totient theorem, Fermat–Euler theorem, Fermat's little theorem, induction, number theory, prime number, whole number

Thursday, 19 January 2017

Problem 19

Find the last digit of 2⁹⁹⁹.

Posted by Từ Nguyên Học at 15:44 No comments:

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Labels: Chinese remainder theorem, Fermat's little theorem, induction, number theory, prime number, 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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Problem 26

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Problem 19

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Problem 27

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Problem 8

Fill in the missing digit to make the number 865* divisible by 7.
Problem 24

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Problem 7

Fill in the missing digits to make the number 766776** divisible by 11.
Problem 31

A two-digit integer n has the property that the sum of n and its digits is equal to 63. Find n.
Problem 20

Find the last digit of 43 4 3 .
Problem 25

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

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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 4
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  - Problem 1

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