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roger
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My mind has gone fallow, and I can't quite understand factoring a number into two coprime numbers.
What happens if the number of divisors is odd?
What happens if the number of divisors is odd?
roger said:(but this particular case has an even number of divisors(of 3^3 * 5^2 * 7^5) right?)
matt grime said:I don't think that is what your book says at all. Or at least it is not all it says. Take the sequence a_n=2n. Then mod 4 the sequence goes
0,2,0,2,0,2,0,...
I don't see anything that could be described as a 'consecutive pair of residues'.
roger said:No. I don't know in what sense (mathematically) (0,1) and (1,0) are 'different'.
and again, no I don't know the pigeon hole principle.
I asserted that the answer ought to be =>(n^2)+1 because I thought if there were n^2 pairs of residues,
then the next term would create a pair which is a duplicate.
But there needs to be 2 more terms than n^2 to create a duplicate. Yet I still don't understand how it works.
consider the sequence of integers 2,3,5,8,10,12.
Then mod 2 the sequence goes 0,1,1,0,0,0. Yet there is no 2 pairs of integers here despite the original sequence being greater than n^2+1 terms, in this case 6>5. Why not?
read posts 16 and 18 again, and this one several times. try to think about what is going on.I don't see the relevance of this: '' you need 2 terms to get one pair, 3 terms to get 2 pairs and so on''
Thanks
roger
When we say that the mind has gone fallow, we are referring to a state of mental inactivity or stagnation. It is a term often used to describe a lack of inspiration or creativity.
A fallow mind can make it difficult to understand factoring because it can hinder our ability to think critically and problem solve. When our minds are not actively engaged, we may struggle to grasp new concepts or make connections between ideas.
Yes, a fallow mind can be a temporary state. It is often a result of mental fatigue or a lack of stimulation. Taking breaks, engaging in activities that promote creativity, and getting enough rest can help refresh the mind and overcome a state of mental fallowness.
While a fallow mind can be frustrating, it can also have some benefits. It allows our brains to rest and recharge, which can improve overall mental well-being. It can also provide a break from constant mental stimulation, allowing us to come back to tasks with a fresh perspective.
To overcome a fallow mind and improve understanding of factoring, it is important to engage in activities that stimulate the mind, such as reading, solving puzzles, or engaging in creative hobbies. It can also be helpful to take breaks and get enough rest to avoid mental fatigue. Additionally, seeking help from a tutor or mentor can provide additional support and guidance in understanding difficult concepts.