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devious_
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Find all integers n>1 such that n is a power of 3, and n-1 is five times a power of 2.
Can anyone give me a push in the right direction?
Can anyone give me a push in the right direction?
TenaliRamanTenaliRaman said:First transition :
Binomial expansion
Second transition :
Cancelling 1 from both sides
Third Transition :
Take 80 common on the LHS and divide both sides by 5
Fourth Transition :
divide both sides by 16 (2^4 = 16)
-- AI
Modulo arithmetic is a mathematical operation that calculates the remainder after dividing two numbers. It is denoted by the symbol "%". For example, 7 % 3 = 1 because 7 divided by 3 leaves a remainder of 1.
Modulo arithmetic has various applications in fields such as cryptography, computer science, and engineering. It is used to generate random numbers, detect errors in data transmission, and perform calculations in digital circuits.
In regular arithmetic, the result of a division will always be a whole number. In modulo arithmetic, the result is always the remainder after division. Additionally, in regular arithmetic, the numbers can be both positive and negative, while in modulo arithmetic, they are always positive.
The modulus is the number that defines the size of the group in which the operations of modulo arithmetic are performed. It determines the range of values that the remainder can take. For example, in the equation 7 % 3 = 1, the modulus is 3.
Most programming languages have a built-in operator for modulo arithmetic, denoted by the symbol "%". You can also use the modulo function or method, depending on the language. For example, in JavaScript, you can use the modulo operator (%), while in Python, you can use the modulo function (mod).