Find counterexample for statement
2^2 +3^2 is divisible by 4
the key n=3
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myininaya (myininaya):
4+9=13
13 isn't divisible by 4
OpenStudy (anonymous):
Well 4 can't divide 4 +9 =13
OpenStudy (salina):
sorry \[2^n+3^n\] not 2^2+3^2
OpenStudy (anonymous):
Ohhh I see
myininaya (myininaya):
i cant read
both have same exponent right?
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OpenStudy (anonymous):
ahun to the power of n
OpenStudy (salina):
yes,
myininaya (myininaya):
2^3+3^3=8+9=17
4 doesnt divide 17
this is one counterexample
OpenStudy (salina):
the key is n=3 divi by 4
OpenStudy (anonymous):
myininaya what is counterexample ?
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myininaya (myininaya):
giving an example of showing a statement is false
OpenStudy (anonymous):
Okay
OpenStudy (anonymous):
2^3 + 3^3 = 35
myininaya (myininaya):
2^1+3^1=2+3=5
5 is not divisible by 4
this is another counterexample
OpenStudy (anonymous):
yeah which is still not divisible by 4
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myininaya (myininaya):
what do you mean the key n=3?
OpenStudy (salina):
the question has key answer n= 3
OpenStudy (anonymous):
You Put anything instead of n but you won't get it divisible by 4 ...maybe that's what I think ...the problem lies in three
\[\frac{(2 \times 2 \times 2 \times ...n) + ( 3 \times 3 \times .....n)}{4} \]
myininaya (myininaya):
there are other n's like n=1
myininaya (myininaya):
and n=2
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myininaya (myininaya):
2^4+3^4
=16+81
=97
97 isn't divisible 4
do you have enough counterexamples?
lol