Final answer:
Without the context of 'problem 26', it's not possible to demonstrate that p ≡ 1 (mod 4) with the given information. Typically, prime numbers of the form 4k+1 are congruent to 1 modulo 4, but the value of p provided appears to be a probability, not an integer suitable for modular congruence.
Step-by-step explanation:
To demonstrate that p ≡ 1 (mod 4) for a certain value of p described in 'problem 26', we should first understand what is provided in Solution 8.13. However, since the context of 'problem 26' is missing in the information provided, it's not possible to directly show why p satisfies the congruence p ≡ 1 (mod 4). Nevertheless, a number being congruent to 1 modulo 4 generally means that when that number is divided by 4, the remainder is 1. This is typical for prime numbers of the form 4k+1. For instance, prime numbers like 5, 13, 17, etc., are all congruent to 1 modulo 4.
However, the p calculated in Solution 8.13 seems to be a probability (approximately 0.278) rather than an integer that could be evaluated for congruence modulo 4. Therefore, with the information provided, the statement p ≡ 1 (mod 4) does not seem applicable, and we'd need a proper definition of p from 'problem 26' in order to show the congruence relation.