Assertion: remainder | /r/HasProperty | equivalent
Facets:
value: to the remainder of 2
type: OTHER
value: for any polynomial #f(x
type: OTHER
value: to 1
type: OTHER
Source sentences:
text: your 2^9 remainder is equivalent to the remainder of 2^1.
text: When dividing by d, either both remainders are positive and therefore equal, or they have opposite signs.
text: If two integers are equal, then all their residues are equal.
text: your remainder will be equivalent to the remainder of 2^4 which would equal 16
text: your remainder will be equivalent to the remainder of 2^6.
text: out.since the pattern repeats every 8 exponents, just divide 9 by 8 to get 1.something.take the integer part and multiply it by 8 to get 8.subtract 8 from 9 to get 1.your 2^9 remainder is equivalent to the remainder of 2^
text: and they want to know what the remainder is.take the exponent of 20 and divide it by 8 to get 2.5take the integer part of the answer and multiply it by 8 to get 2 * 8 = 16subtract 16 from 20 to get 4.your remainder will be equivalent to the remainder of 2^4 which would equal 16again
text: take 2006 and divide it by 8 to get 250.75multiply 8 by 250 to get 2000.subtract 2000 from 2006 to get 6your remainder will be equivalent to the remainder of 2^
text: For example, to test if an integer is odd, one might be inclined to test if the remainder by 2 is equal to 1:
text: The remainder theorem tells us that for any polynomial #f(x)# , if you divide it by the binomial #x-a# , the remainder is equal to the value of #f(a)# .
text: This pattern is the same for any x < 11 (the remainder will just be equal to x).
text: Conversely, if all residues are equal, then the two integers are equal, or their differences is a multiple of M.