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Prove that the expression
is a multiple of
for all natural numbers
find all (x,y)
Solve in integers the following equation
Find all the real a,b,c such that the equality
is valid for all the real x,y,z.
im so sory TheDude and mathsyperson I agree with you
yes i forget Adding 14^1987 to the original sum
no no no
The sum divisible by 15
Prove that
is divisible by .Find integer solutions (x,y) of the equation (1964 times "sqrt"):
.but
But I'm unable to verify
Any suggestions?
Refer to the diagram of the circle inscribed in a
quadrilateral ABCD with the points of tangency at M, N, P,
and Q. For each positive integer n, a diagram is drawn like
this in which lengths of line segments are
AQ = AM = n,
BM = BN = n + 1,
CN = CP = n + 2, and
DP = DQ = n + 3.
The radius of the circle is
Solve the cryptorithm
, where each of a, b, and c is a distinct decimal digit.In the 5 by 5 array, the numbers in every row, every column and both diagonals
form arithmetic progressions.
You are given that
. Find the sum of the 25nice JaneFairfax
thank you
solve the inequalty
where b is real parameterFive ants are on the corners of an equilateral pentagon with side of length 1. They each crawl directly towards the next ant, all at the same speed and traveling in the same orientation. How long will each ant travel before they all meet in the center?
Show that if
is odd,then the last 2 digits of
must be 28.
It is well known that a number is divisible by 9 if and only if the sum of the digits is divisible by 9. For example,
is divisible by 9, and 396 = 9 x 44. Let's introduce the operator as one that sums the digits in a number, so that . With all this in mind, can you determine the value of ?For any
, show that
is always divisible by 2008
Six students visited the library on the day a rare book was stolen. Each student entered once, stayed for some time, and left. For any two of them that were in the library at the same time, at least one of them saw the other. The dean questioned the students and learned the following:
Student Reported seeing
Alice Bob, Eve
Bob Alice, Frank
Charlie Doris, Frank
Doris Alice, Frank
Eve Bob, Charlie
Frank Charlie, Eve
The dean believes that each student reported all the others that he or she saw, with the exception of the thief who, in an attempt to frame another student, reported that other student as being seen when that other student was not in fact in the library. Assume the dean's belief is correct. Can the dean determine the thief?
How many triangles are there with integer sides and perimeter 2007? How many of these are equilateral? How many are isosceles? How many are scalene
For a positive integer,
, we define N! (read N factorial) toSolve the equation
when I take my dog for a walk," said a mathematical friend, "he frequently supplies me with some interesting puzzle to solve. One day, for example, he waited, as I left the door, to see which way I should go, and when I started he raced along to the end of the road, immediately returning to me; again racing to the end of the road and again returning. He did this four times in all, at a uniform speed, and then ran at my side the remaining distance, which according to my paces measured 27 yards. I afterwards measured the distance from my door to the end of the road and found it to be 625 feet. Now, if I walk 4 miles per hour, what is the speed of my dog when racing to and fro?"
Mark is taking a trip and is taking along exactly $1020 in cash. His
father gives him cash for the trip in denominations of 20 dollar bills
and 50 dollar bills only. How many denominations of each
($20's and $50's) are possible?
Form a nine digit number using the digits 1 through 9 exactly once, such that the first (leftmost) eight digits form a number divisible by 8, the first seven digits form a number divisible by 7, and so on.