is an even number a number that can be evenly divided or a number that can be evenly divided by 2?
397336
even number is a number that can be divided by 2 without reminder, generally it is a number in the form 2n\n\nexample: 2,4,6,8,16,258,26,36, -6, -16....
1143446
I do both of those and I also test numbers for divisibility.  My car license plate has as its numeric part the number 594 which is divisible by 11, that's how I remember my license plate number.  Also, when someone asks me to pick a number between 1 and 10, I usually pick pi, phi, or e, just to be a smart@$$.  They didn't say an INTEGER between 1 and 10, did they???
630729
2.Only even number to be prime
471544
Technically it is 3\n\nMultiplication/division always comes before addition/subtraction, so that question becomes half of two (1) plus 2 (1+2=3).\n\nIf you were to bracket the (2+2) on the other hand, then the equation would become half of (2+2) = half of 4 = 2\n\n\nEdit: Haha, cheers aphanes.
475186
A quantity that is divided by another quantity.
894091
None. Two odds make an even
930195
yes because any number ending in zero is even but is divisable by five
885409
A number that can be written as a fraction.
90357
F- even and odds.  There are 3 even sides and 3 odd sides. So the likelihood is the same for both.
620569
A number whose factors (other than itself, of course) add up to the number.\n\nExample : 28, since 1+2+4+7+14 = 28.\n\nEDIT : Here's a nice, detailed article on the history of perfect numbers : http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Perfect_numbers.html\n\nAnd here's an entry from the largest math encyclopedia evar : http://mathworld.wolfram.com/PerfectNumber.html\n\nP.S. One of the great mysteries in math is whether there exists an odd perfect number. Figure it out, and you'll be famous forever :)
927926
"A factor of a number is any integer by which the number can be divided evenly, with no reminder.  The factors of 6, for example,  are\n1,2,3,and 6, . . ."\nFor more details you may wish to consult Encarta encyclopedia--factoring in algebra.
20180
You can't divide by 0, you can divide anything by 1, you can divide any even number by 2 to get a whole number,...etc. This website has more divisibility rules: \nhttp://mathforum.org/k12/mathtips/division.tips.html
476243
1 1/2\n\nboth a whole number and a fraction
928861
if x is odd then\n\nx^n is odd say 2n+1\n\n2n+1 = (n+1)^2 - n^2 \n\nthe it can be done\n\nif x is even then x^n is divisible by 2^n\n\nif n =1 or 2 this is not always true for example\n\n2 is not difference of any 2 squares nor is 4\n\n\nbut for other n it is true\n\n2^n = (a+b)(a-b)\nwe can factor 2^n into 2 distinct even numbers  a+b and a-b from which a and b can be found out.\n\n(if both are not distinct then a-b = a+b or b = 0)
779216
Each digit is even\nEach digit is different\nThe number has 4 digits\nIt is divisible by 4.\nIt is not divisible by 8.\nIt is a square.\n\nYour answer must be: 6084\nIt is the square of 78.\nAll digits are even and different.\nIt is divisible by 4.\nIt is not divisible by 8
995077
Every even integer greater than 2 can be written as the sum of two (not necessarily distinct) primes.
169785
if you require x and y to be even then a and b will also be even: then the answer is no.  \n\na squared even number will always be even, a squared odd number will always be odd.  even + even = even (therefore the first formula can't hold true with your statement).  Similarly, the second formula will also not be true.  even - even = even.\n\nI hope this is what you were looking for, I was a little confused by your statement.  A more general solution exists for x=0 and y=a, y=b... as you stated but this doesn't follow your even/odd request.\n\nGood luck.\n\nEDIT: with your updated comment, I agree.  x=0 is still a trivial solution.  You could do a quick program and have it solve for the equation using brute force, if you find a hit you can use "Proof by Example".\n\nI'm guessing the problem isn't solvable though and you need to prove why... my discrete math is a bit rusty though, try focusing on the properties of the equation... possibly solve it graphically by comparing the expanded triangle equations.\n\nPS. it looks like the problem is solvable if both sides are perfect squares and the opposite is the square root of the sum of two squares: x^4 + y^4 = a^2 * b^2\n\nEDIT2: look at the proof of why it is impossible to make a Heronian triangle from two pythagorian triangles.  I think this will help you :-)\n\nGood luck.