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Prove that the square of any odd number is always 1 more than a multiple of 8.
Find
if
.How many even integers between 4000 and 7000 have all digits different?
nice mathsyperson
but how
find x
Let ABC be an isosceles triangle with AB = AC. Let X ad Y be points on sides
BC and CA such that XY // AB. Denote by D the circumcenter of triangle
CXY and by E be the midpoint of BY . Prove that m(AED )= 90°.
Suppose that the real numbers
satisfying
Evaluate the sum
Suppose r is a root of the polynomial
let
integersand
prove that
divisible by , OR OR divisible by
In how many ways can one distribute 6 apples, 7 bananas, and
8 cantaloupes between 10 people? All fruit of the same type are identical.
Fruit must remain whole, must all be given out, and possibly Alphonse gets
everything.
jane and olivia both celebrate their birthday today. In three years, jane
will be four times as old as olivia was when jane was two years older than
olivia is today. If olivia is a teenager, how old is jane now?
Solve the equation
Find the minimum value of
.What is the remainder when
6^83 + 8^83 is divided by 49?
solve in integers
Prove that if
Fill in the Magic square 5×5 with numbers from 1 to 25 such that the side totals and diagonal totals equal 65.
Let integer p and q
Prove that
Very nice work Jane thank you
For how many positive integers n is
an integer ?
Suppose
are n × n matrices with entries in a feld F,satisfying the conditions that
andare symmetric and
Here I is the n × n
identity matrix, and if M is an n × n matrix,
Prove that
It is possible to replace each of the ± signs below by either – or + so that
± 1 ± 2 ± 3 ± 4 ± ... ± 96 = 1996.
At most how many of the ± signs can be replaced by a + sign?