Which of the following is a Pythagorean triple?
a. 6, 8, 12
6² + 8² =
36 + 64 =
100
12² =
144
100 does not equal 144, so this
is not a Pythagorean triple.
b. 3, 4, 5
3² + 4² =
9 + 16 =
25
5² =
25
These are both 25 and are both equal,
so this IS a Pythagorean triple.
c. 1, 2, 3
1² + 2² =
1 + 4 =
5
3² =
9
5 does not equal 9, so this is not a
Pythagorean triple.
d. 5, 7, 12
5² + 7² =
25 + 49 =
74
12² =
144
74 does not equal 144, so this is not a Pythagorean triple.
So the answer is b
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Which of the following remains an unsolved problem in mathematics?
a. Konigsberg Bridge Problem
No for it can be proved that this can be done if there are
an even number of bridges to cross and not if there are an
odd number of bridges.
b. Fermat’s Last Theorem
Yes, this was solved by Wiles in the 90's. It states that if
4 positive integers exist a, b, c, n so that an + bn = cn,
then n must either be 1 or 2.
c. Goldbach’s Conjecture
No, this states that every even positive
integer greater than 2 is the sum of two
prime numbers. It has not been solved.
D. Fundamental Theorem of Arithmetic
This is that every positive integer has
one and only one prime factorization.
It has been proved.
So the answer is c.
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Which is the third row of Pascal’s triangle?
Pascal's triangle is
1 < - first row
1 1 < - second row
1 2 1 < - third row
1 3 3 1 < - fourth row
1 4 6 4 1 < - fifth row
1 5 10 10 5 1 < - sixth row
· · · · · · ·
The third row is 1 2 1
a. 1 1 b. 1 4 6 4 1
c. 1 2 1 d. 1 3 3 1
So the answer is c.
However, some authorities do not count the
top row consisting of only the number 1.
If your teacher is one of these, then the
answer is 1 3 3 1, or d.
Edwin