Given a number N and a digit D, can you find an expression that
contains only D and the operators +, -, *, / and concatenation
Concatenation (+) is the operation of joining two numbers or strings end-to-end. For
example, the concatenation of '4' and '9' is '49'.
and evaluates to N?
Quadratic Equation Solver
Chinese Remainder Theorem
In number theory, the Chinese remainder theorem states that if one knows the
remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the
remainder of the division
of n by the product of these integers, under the condition that the divisors are pairwise co-prime. You can read
up on its proof here.
GoldBach Conjecture
Goldbach's conjecture is one of the oldest and best-known unsolved problems in
number theory and all of mathematics. It states that every even whole number greater than 2 is the sum of two
prime numbers. The conjecture
has been shown to hold for all integers less than 4 × 1018, but remains unproven despite considerable
effort.
Kaprekar's Constant
Type in any 3 or 4 digit number which isn't a monodigit (something that's not like
1111 or 222). If the difference between the descending and ascending orders of the number results in a
monodigit, the number won't work
either.
The difference between the descending and ascending orders of the number will eventually reach 6174 in case
of 4 digits or 495 in case of 3 digits, aka Kaprekar's Constant.
Collatz Conjecture
The Collatz conjecture is a conjecture in mathematics that concerns the following
sequence.
Enter any positive integer n. Then, if the previous term is even, the next term is one half of the previous
term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that no
matter what value
of n, the sequence will always end at 1. Try it out!
'→' signifies the operation ((n × 3) + 1)
'→' signifies the operation (n ÷ 2)